Introduction: Yes, we have subjunctives in English, and you probably use them every day, much more than you realize.  But because you probably don't realize you are doing it, trying to use the English subjunctives to help you learn the German seems likely to produce more confusion than anything else. Just focus on the German! Then, after you understand the German, you may find it interesting to use the German to help you realize what you are doing in English.

I. Terminology

The subjunctive is a mood, not a tense. Verbs have three moods: indicative, imperative, and subjunctive. The basic idea of the subjunctive is that it expresses situations that are, or may be, contrary to fact.

German has two subjunctives. Each of them has present and past tenses. Each of them has several names. We will use the English and German terms in bold, but in other sources you may see other terminologies.

Subjunctive I / Konjunktiv I (special subjunctive) is formed from the present tense and is, therefore, sometimes called the "present subjunctive." It is used much less than Konjunktiv II.

Subjunctive II / Konjunktiv II (general subjunctive) is formed from the past tense and is, therefore, sometimes called the "past subjunctive."

To avoid confusion, it is best to refer to the tenses of the subjunctives as "present-time subjunctive II," "past-time subjunctive II," and so on.

II. Forms of the subjunctive II
 

The subjunctive endings.

ich -e wir -en

du -est ihr -et

er/sie/es -e sie -en
 

A. Subjunctive II -- present time

Regular verbs.

To the stem, add the -t- of the simple past, plus the subjunctive ending. This produces a form that looks just like the simple past.

Example: take machen. The stem is mach-. Add the -t- and the personal ending -e, and you get er machte, which looks just like the simple past.

Irregular verbs: general rule.

To the stem of the simple past, add the subjunctive endings. Umlaut the stem vowel if possible, i.e. if it is a, o, or u.

For example: take sein. The simple past is war. Umlaut the a, add the subjunctive endings, and you get
 

ich wäre wir wären

du wärest ihr wäret

er/sie/es wäre sie wären.
 

Note that although war is an irregular form, the derivation of the subjunctive from war is completely regular. The same applies to haben (simple past: hatte).
 

ich hätte wir hätten

du hättest ihr hättet

er/sie/es hätte sie hätten
 

Most irregular verbs work this way. Once you know the irregular simple past form, the formation of the subjunctive from that is perfectly regular. A few irregular verbs form their subjunctives in unusual ways.
 

Unusual irregulars.
 

A very few strong verbs have irregular subjunctives: helfen - hülfe, sterben - stürbe, werfen - würfe. For helfen, hälfe is also used. Stehen can be either stände or stünde.
 

Mixed verbs.

Umlaut the stem vowel of the simple past. But for brennen, kennen, nennen, senden, wenden and similar verbs, spell the altered vowel as e, not ä.

Examples: denken - dächte, bringen - brächte, but brennen - brennte, nennen - nennte.
 

Modal verbs.

Umlaut the stem vowel of the simple past, except with wollen and sollen (with them, the subjunctive looks just like the simple past).

Example:
 

ich könnte wir könnten

du könntest ihr könntet

er/sie/es könnte sie könnten.
 
 
 

B. Subjunctive II -- past time
 

For all verbs, take the present perfect, and use the correct subjunctive II form of the auxiliary verb. Examples:
 

ich hätte gemacht   (Present perfect is ich habe gemacht)

du wärest gekommen

er hätte gearbeitet

wir wären gewesen
 

C. würde-paraphrase
 

For all verbs, an alternative to the present-time subjunctive II is formed by using the subjunctive II of werden with the infinitive. Ich würde gehen. Er würde sein. Sie würden kommen. The würde-paraphrase is identical in meaning to the subjunctive II of the main verb: ich würde gehen means exactly the same thing as ich ginge. Usage will be discussed below. 

III. Use of the Subjunctive II

The basic idea of the subjunctive is that it expresses situations that are, or may be, contrary to fact. When we use the indicative, we assert that something is a fact; when we use the subjunctive we assert that something might be a fact (or might not be), that we would like for something to be a fact (but it isn't), that something might be a fact under certain circumstances. Derived from this basic idea of subjunctiveness are the uses of the subjunctive for politeness and to express indirect quotations.

In this section, the subjunctive II and the würde-paraphrase are treated as identical. The subjunctive II is used in the following situations.
 

A. Hypothetical statements and questions.

Das wäre schön.

Was möchtest du tun?
 

B. Unreal or contrafactual conditional sentences.

Wenn wir genug Geld hätten, würden wir im Sommer nach Deutschland fahren.

The implication is that we do not have enough money, but if we did, we would go to Germany.

Distinguish this from the indicative sentence

Wenn wir genug Geld haben, fahren wir im Sommer nach Deutschland.

We may have enough money, we don't know yet for sure, but if we do, we will definitely go to Germany.

NOTE: English usage is exactly parallel to German in sentences like these.

Subjunctive: If we had enough money, we would go to Germany in the summer.

Indicative: If we have enough money, we will go to Germany this summer.

(See "Do we have the subjunctive in English?" below.)
 

Such conditional sentences do not always involve the two-clause, if . . . then construction. Consider these examples (from Durrell 212):

Bei dem Wetter wäre ich nicht in Urlaub gefahren.

Ich würde sonst das Fenster aufmachen.

Ich hätte schon an sie geschrieben, nur habe ich ihre Adresse nicht gewußt.
 

C. Wishes.

Wenn ich nur reich wäre!

Ich wünschte, wir hätten mehr Zeit.
 

D. Clauses following als ob and other conjunctions meaning as if.

Er gibt Geld aus, als ob er reich wäre.

Er redet, als ob er ein großer Expert wäre.
 

E. Politeness subjunctives, used "to moderate the tone of an assertion, a statement, a request or a question and make it sound more polite" or less assertive.⁽¹⁾ This is extremely common in all types and levels of German. If anything, it is more common in colloquial German than in more formal German.
 

Könnten Sie mir sagen, wie ich zum Bahnhof komme?

Verkäuferin (etwa in der Bäckerei): Sonst noch etwas? Kunde: Nein, das wäre es für heute.

Ich hätte gern ein Wienerschnitzel mit Pommes.

Würdest du mir das Brot reichen?

Könnten Sie mir bitte helfen?
 

F. Achievements after difficult or delay. (See the discussion at canoo.net.)

The subjunctive may be used to express that something has been achieved, but only after difficulty or delay.  The situation is not hyopthetical or contrary to fact; the subjunctive seems to express that the situation was almost contrary to fact, or was contrary to fact for a long time.

Examples from canoo.net:

Da wäre dann endlich Ihre Bestellung!      =     Hier ist endlich Ihre Bestellung.
Das hätten wir geschafft!      =     Wir haben es geschafft!
Somit wäre dieses Problem gelöst.      =     Somit ist dieses Problem gelöst.

G. Expresion of doubt in questions or statements.  (See the discussion at canoo.net.)

It is a short step from the use of the subjunctive for hypotheticals to its use to express doubt, or to indicate that you are assuming something to be true, but aren't really certain about it. 

Examples from canoo.net:

H. Clauses after als dass, ohne dass (examples adapted from Durrell 214):

Diese Stereoanlage ist viel zu teuer, als dass ich sie mir leisten könnte.

Diese Mannschaft ist seit Jahren in der Bundesliga, ohne dass sie je deutscher Meister geworden wäre.
 

The subjunctive in such clauses is rather formal; colloquial German would usually use the indicative.

IV. One-word subjunctive or würde-paraphrase?

As noted above, there is no difference in meaning between, for example, er führe nach Deutschland and er würde nach Deutschland fahren. A speaker's choice of one form or another is determined by a variety of factors, including stylistic register, the particular structure being used, the verb involved, and perhaps other factors, including the speaker's level of education.⁽²⁾
 

A. Since regular (weak) verbs have subjunctive II forms that are identical to the simple past, they tend to be used in the würde-paraphrase. In informal situations, the würde-paraphrase is nearly always used for weak verbs. In more formal writing and speech, the subjunctive of a weak verb is occasionally used, if the context makes clear that the form is subjunctive. (For example, in a wenn/dann sentence, if just one of the verbs is a clear subjunctive, that makes clear that the other one must be subjunctive, too, so a regular verb could be used in its one-word subjunctive form, as in Wenn ich länger arbeiten würde, verdiente ich kaum mehr Geld (example from MGG p. 101). 
 

B. In wenn . . . dann conditional sentences, there is something of a tendency, apart from all other issues, to use one-word forms in the wenn-clause and würde-forms in the dann-clause: Wenn er mehr Zeit und Geld hätte, würde er öfter in Restaurants essen. But this is by no means a requirement.
 

C. With haben, sein, werden, and the modals, the würde-form is very rarely used in any type of German. 

E. With a few strong and other irregular verbs, one-word forms and würde-forms are used about equally often. These include käme, täte, wüsste in all types of German, and fände, gäbe, ginge, hielte, hieße, ließe, and stünde in all but the most colloquial, i.e. in R3 and R2.
 

F. With other strong verbs, the one-word forms are used primarily in more formal types of German, especially written German, and the würde-forms are far more common even then. The one-word subjunctive II forms of many less common strong verbs are very rare, even in the most formal writing, though they will be found occasionally.
 

G. IN SUM, the following simplified rules of thumb are a good guide to usage:

a) Always use the one-word subjunctive II, never the würde-form, of haben, sein, werden, and the modals.

b) Don't even consider the würde-form for the fixed expressions listed in D.

b) Use the one-word subjunctive II forms for the verbs listed in E if you want to, especially in writing and in wenn-clauses, but don't hesitate to use the würde-form if you prefer.

c) For all other strong and irregular verbs, and for weak verbs, use the würde-form all the time.
 

H. Note: würde+infnitive is not always a paraphrase.  

1) Würde+infinitive also has a use for referring to the future in a narrative about the past.   

At that time I didn't know yet how weak I am: I didn't know that I would be afraid. I could not imagine what this night would make of me . . . .

A discussion at http://www.babelboard.de/showthread.php?t=5723 suggests a difference between sollte and würde for references to the future in the past, with sollte implying more certainty, and only würde making sense after ob, while both work after dass. This seems to make sense.

Er wusste damals nicht, dass sein Buch sehr erfolgreich werden würde.

Er wusste damals nicht, dass sein Buch sehr erfolgreicht werden sollte. 

Er wusste damals nicht, ob sein Buch sehr erfolgreich werden würde.

This is a very standard construction, but grammar sources say amazingly little about it. Both canoo.net (http://www.canoo.net/services/Controller?input=sollen&service=canooNet) and the 4th edition of the Duden Grammatik (S. 102) discuss the usage of sollen, but not würde for "Zukunft in der Vergangenheit." Grimms Deutsches Wörterbuch does devote a section of its entry on werden to  "präteritale konjunktivformen von werden mit einer verbalen grundform, die zukunft von einem standpunkt der vergangenheit aus bezeichnend" (http://germazope.uni-trier.de/Projects/WBB/woerterbuecher/dwb/wbgui?textsize=600&mode=hierarchy&onlist=GW16800,3&lemid=GW16800#GW16800L78).

2) Forms of würde are also used to form subjunctive forms of the passive voice. Don't worry about that for now.

V. Subjunctive I - present time
 

For all verbs except sein, add the subjunctive endings to the present tense stem. This produces forms that are identical to the present indicative, except in the 3rd person singular and, for some verbs, the 2nd person singular. The subjunctive I is, therefore, virtually never used except in the 3rd person singular, where the forms are very distinctive: er habe, sie gehe, es gebe.

Sein has the irregular 1st and 3rd person singular form sei. Otherwise it is regular.

ich sei wir seien

du seiest ihr seiet

er/sie/es sei sie seien
 

Subjunctive I -- past time
 

For all verbs, take the present perfect, and use the correct subjunctive I form of the auxiliary verb. As with the present time subjunctive I, only the third person singular is normally used. Examples:
 

er habe gemacht

er sei gekommen

er habe gearbeitet

er sei gewesen
 
 
 

VI. Use of subjunctive I

1. Expressions of wishes and desires and hopes that may be fulfilled (as opposed to contrafactual wishes and desires that would be expressed with subjunctive II). 

Some such expressions are very much a part of everyday language:

Gott sei Dank!

Others sound rather formal:

Möge Ihnen das neue Jahr viel Glück bringen!
 

      Möge has a usage similar to that of "shall" in English legalese. An example from a motion reported in the minutes of a student organization: 

                      Der AStA möge beschließen, eine Drum'n'Bass-Party in Höhe von 350 Euro zu fördern und davon 150 Euro als Vorschuss auszuzahlen.

                            (http://www.asta.uni-potsdam.de/dokumente/index.php3?textfile=944)
 

2. In instructions, recipes, and the like:

Man nehme zwei Eier und 250 Gramm Mehl.
 

3. In technical or academic writing, in sentences like this:

Ein Beispiel sei gegeben.

Hier sei nur ganz kurz auf die bahnbrechende Arbeit von Hugeldubel verwiesen.
 

4. In a few idioms like

Wie dem auch sei ( be that as it may).
 

5. In indirect discourse.
 
 
 

VII. Indirect discourse and the subjunctive
 

Direct quotation repeats exactly what another person said, using quotation marks in writing or some equivalent in speaking. Indirect speech reports another's words without the quotation marks, and without the same assertion of exactness.

Direct: She said, "I want to go home."

Indirect: She said she wanted to go home.

She said that she wanted to go home.
 

All but the most colloquial German routinely uses the subjunctive to quote indirectly. Even in colloquial spoken German, a subjunctive is frequently used, though not always. Written German uses the subjunctive I extensively in indirect speech.  The subjunctive is used to indicate that the speaker is not asserting that the statements are true, but rather that someone else has asserted that they are true. However, it does not necessarily imply that the speakers doubts the truth of the statements. 

There is a good deal of variation in usage, but the basic rules are as follows.
 

1. The tense of the original statement is kept in the indirect quotation (unlike in English), except that all the past tenses of the direct quotation correspond to the past-time subjunctive in indirect speech.
 

2. Subjunctive I is used, if a distinctive form exists (i.e., for most verbs, only in the third person singular). The tense of the original statement is kept.
 

Frau Blum: "Ich weiß es schon."

Frau Blum sagte, sie wisse es schon.
 

Frau Braun: "Ich habe ihn 1945 geheiratet."

Frau Braun sagte, sie habe ihn 1945 geheiratet .
 

3. If no distinctive form exists in subjunctive I, then subjunctive II is used.
 

Frau Blum und Frau Braun: "Wir wissen es schon."

Frau Blum und Frau Braun sagten, sie wüßten es schon.
 
 
 

This pattern is extremely common in written German, especially in journalism. Examples can be found in any newspaper. However, the pattern is also sometimes varied, with subjunctive II used where the rules would predict subjunctive I, and the indicative sometimes used as well. Discussing these variations would only confuse the issue at present. It should be noted, however, that these variations are purely matters of style--they do not indicate more or less faith in the truth of the statements quoted, or anything like that.
 

In less formal writing and in more formal speech, the subjunctive I is used much less. It may be limited primarily to sein and haben. Subjunctive II generally replaces subjunctive I, and the würde-paraphrase tends to be used rather than the one-word subjunctive forms.
 

In really colloquial speech, the subjunctive I is not used at all. The subjunctive II is often used, generally in the würde-paraphrase except with a few common verbs, but the indicative is used more often than the subjunctive. The subjunctive is most likely to be used in a long strech of indirect speech, as in this example (adapted from Durrell 212): Karl sagt, dass er einen neuen Wagen gekauft hat. Der hätte über 50 000 Mark gekostet und hätte eine Klimaanlage.
 
 
 

IV. Do we have the subjunctive in English?
 

Do we have the subjunctive in English? Yes, and we use it all the time, in much the same way as it is used in German. However, much more often than not, the subjunctive looks and sounds just like some other verb form.
 

Just as in German, we have two subjunctives. One is derived from the simple past tense, like the German Subjunctive II. For most verbs, it is identical to the simple past. If I had enough money, I would go to Germany every summer. If she ran a little faster, she would be unbeatable. But to be has distinct subjunctives in the first and third person singular: I were (simple past was), he/she/it were (simple past was). If I were you, I wouldn't do that. Another subjunctive is derived from the present tense, like the German Subjunctive I. Like its German counterpart, it has a distinctive form only in the third person singular: he have, she drive, it sponsor. Here, again, to be is different, and uses be in all persons and numbers as a subjunctive: Be that as it may. Far be it from me to . . . . We also frequently paraphrase the subjunctive with would (or should) plus an infinitive, as in the clauses with would go and would be above.
 

In English, we use our "Subjunctive II" mainly in conditional sentences (as in the examples above) and to express situations contrary to fact: I wish I were rich. This is perfectly normal, everyday English. You can't substitute the present tense at all in many cases. *If I have enough money, I would go to Germany every summer just sounds nonsensical. If I have enough money, I go to Germany every summer has a different meaning. ?If I would have enough money, I would go to Germany every summer may be grammatical, but also may sound a little odd. The simple past is sometimes substituted for the "subjunctive II" of to be: If I was you, I wouldn't do that. I wish I was rich. This may be regarded as informal, colloquial, or substandard, but speakers who use the simple past in these constructions are still using a distinct verb form to express "subjunctiveness." You might say If I were you or If I was you, but you will not say *If I am you, I wouldn't do that.
 

We use our "Subjunctive I" mainly in "recommendations, resolutions, commands, and statements of necessity" (Cook 197): The dean recommends that the department offer an evening course. This may seem rather formal, but the indicative offers is impossible here. The less formal alternatives are completely different, for example: The dean asks the department to offer an evening course. The usage is by no means limited to learned or academic language. Here's an example from USA Today: Vice President George Bush phoned Noriega . . . asking that Noriega warn Fidel Castro not to interfere in the operation (quoted in Burchfield 747). Again, the indicative warns would not be possible; the alternative would be asking Noriega to warn . . . .
 

We also use both our subjunctives in a large variety of fossilized expressions and idioms, perhaps without mentally processing the verbs as subjunctives: be that as it may, God forbid, God bless you, so help me God, God damn it, come what may.

1. Quotation from Durrell 214.

2. Durell (209-10) provides an excellent discussion of this matter.

Most if not all elementary German textbooks and surely all textbooks intended for the intermediate level and up contain presentations of the subjunctive. The problem is that the terminology used is often confusing and some of the things said about the usage and even the forms are misleading.
 

An excellent discussion of the forms and especially the usage of the subjunctive in German may be found in

Martin Durrell, Using German: A Guide to Contemporary Usage (Cambridge: Cambridge University Press, 1992), pp. 208-214.

There are citations here to "MGG," which is Bill Dodd et al., Modern German Grammar: A Practical Guide, 2nd edition (Routledge, 2003), and to 

"canoo," which is www.canoo.net, an excellent general reference site for German grammar.

On the English subjunctive, see the following:
 

Burchfield, R. W., ed. The New Fowler's Modern English Usage. 3rd ed. Oxford: Clarendon, 1996.

Cook, Claire Kehrwald. The MLA's Line by Line: How to Edit your Own Writing. Boston: Houghton Mifflin, 1985.

Follett, Wilson. Modern American Usage: A Guide. New York: Hill and Wang, 1966.