You use the subjunctive (II) if you want to express that something is hypothetical, i.e. that something might happen, but there is no guarantee it will, or that something could have happened, but it didn't. The subjunctive is also used for wishes and polite requests. After all, your wish might not come true, and your request might not be fulfilled. So they are hypothetical as well.

You differentiate between a hypothetical future and a hypothetical past.
 

1. The hypothetical future

The hypothetical future is used for:

polite questions: Könnten Sie mir helfen? (Could you help me?) //  Das wäre sehr nett von Ihnen. (That would be very nice of you.)
hypothetical conditions: Wenn ich mehr Zeit hätte, würde ich öfters eine Messe besuchen. (If I had more time I would visit a trade fair more often.)
expressing a wish: Wenn doch nur der Bus käme! (If only the bus would come!)
as-if-clauses: Er sprach so laut, als ob wir alle taub wären. (He spoke so loudly as if we were all deaf.)
 

Note: In German, you always use the subjunctive (II) in the if-clause and in the main clause, e.g.

Wenn ich im Lotto gewinnen würde, könnte ich eine Weltreise machen. (If I won the lottery, I could go on a trip around the world.)

Formation of the hypothetical future/present:

weak verbs: Since the subjunctive (II) forms of these verbs are identical to the simple past forms, one usually uses the alternative construction of "würden" (subjunctive (II) of the verb "werden") + infinitive, e.g.

Wenn er öfter Yoga machte, hätte er keine Rückenschmerzen. -> Wenn er Yoga machen würde, hätte er nicht so oft Rückenschmerzen.
(If he did yoga more often, he wouldn't suffer from a back pain.)

strong & irrregular verbs: Use the "ich-form" in the simple past of the  verb and add the subjunctive (II)-endings (-e, (e)st, -e, -en, et, en). The subjunctive form will usually also have an umlaut if possible.

Since quite a number of these official subjunctive (II)-forms have begun to sound old-fashioned, it has become acceptable to use the alternative construction of "würden" (subjunctive (II) of the verb "werden") + the infinitive for these verbs as well, e.g. "ich würde fahren, du würdest fahren ...." instead of "ich führe, du führest ....".

With some verbs, however, it is still essential to use the proper subjunctive (II)-forms:

Note: The umlaut only ever occurs in the subjunctive (II), never in the simple past.
 

2. The hypothetical past

The hypothetical past is used for speculating about the past e.g.

Was wäre passiert, wenn Stauffenberg mit seinem Attentat auf Hitler im Juli 1944 Erfolg gehabt hätte? (What would have happened if Stauffenberg's assassination attempt on Hitler in July  1944 had been successful?)

Wenn die Musik nicht so laut gewesen wäre, hätten die Nachbarn nicht die Polizei angerufen. (If the music hadn't been so loud, the neighbours wouldn't have called the police.)

Formation of the hypothetical past:

the subjunctive (II)-forms of "haben" or "sein" + past participle
 

If a verb is conjugated with "haben" in the perfect tense, you use the subjunctive-forms of "haben", and if it is  conjugated with "sein", you use the subjunctive (II)-forms of "sein", e.g.