The subjunctive is frequently used in dependent clauses. Clauses are groups of words which express an idea and contain a predicate (i.e., a conjugated verb) and a subject, although of course in Spanish the subject is often merely indicated by the verb ending. They can be divided into two categories: independent clauses (which make sense by themselves) and dependent clauses (which need to be used with an independent clause to form a complete sentece). In general, the indicative, the conditional, and the imperative (command forms) are used in independent clauses; some exceptions will be given below. The subjunctive mood is found primarily in dependent clauses, but of course the other moods can occur there as well, depending on the type of clause, the action/state involved, and its relationship to other elements in the sentences such as the governing verb.

Use of the subjunctive in independent clauses. As already mentioned, the subjunctive is seldom used in main clauses, but there are a few exceptions:

The past subjunctive may be used with the verbs poder, querer, and deber to express courtesy or an attitude of deference.

(Yo) quisiera pedirte un favor.
I'd like to ask you a favor.

Debieras practicar un poco más.
You should practice a little more.

¿Pudieran Uds. darme otros ejemplos?
Could you give me some other examples?

Words meaning “perhaps” (tal vez, quizá, and quizás) may be followed by the subjunctive to suggest that the action or state is improbable, or doubtful; they may also be followed by the indicative to stress a greater degree of likelihood or probability. [Note: The expression for “perhaps” has no effect on the verb if it comes after the verb.]

Quizás participamos en la fiesta.
Perhaps we'll take part in the festival. [Indic.: probable]

Quizás participemos en la fiesta.
Perhaps we'll take part in the festival. [Subj.: doubtful]

Command forms —or imperatives— are based on the subjunctive, with only three exceptions: the affirmative tú forms, affirmative vosotros forms, and the affirmative form for “let's go”, vamos. [Reminder: In Spanish we have command forms for tú, vosotros/as, usted, and ustedes, plus nosotros/as [“Let's ... (do something)”]

Tú: Habla más despacio. Talk slower. [Not based on the subj.]
No hables tan rápidamente. Don't talk so fast. [Subj.]

Usted(es): Díga(n)me la verdad. Tell me the truth. [Subj.]
No me diga(n) mentiras. Don't tell me lies. [Subj.]

Vosotros: Comed con nostros. Eat with us. [Not based on the subj.]
No comáis los huevos. Don't eat the scrambled eggs. [Subj.]

Nosotros: Bailemos. Let's dance. [Subj.]
No bailemos a esa música. Let's not dance to that music. [Subj.]

Vamos al parque. Let's go the park. [Exception, not based on the subj.]
No vayamos al cine. Let's not go the movies. [Subj.]

Noun clauses may function as the object or predicate compliment of a verb. Remember the importance of governing verbs and their effect on subordinate noun clauses: normally verbs such as reporting, affirmation, knowledge and certainty (“think”, “believe”, “affirm”, “be certain of”, etc.), are followed by the indicative. In contrast, the subjunctive is used in dependent clauses following: 1) verbs of influence, such as “urge”, “advise”, “permit”, “forbid”, “ask”, or “want” (someone else to do something); 2) verbs of doubt or denial, such as “doubt”, “deny”, “be unsure of”; 3) verbs of emotion such as “regret”, “be happy”, “be sorry”, “fear”; 4) impersonal expressions indicating these things or subjective reactions, for example, that it is “good/bad”, “(im)possible”, “(im)probable”, “(un)likely” (that something happen).

Yo creo que Juana viene manana. I think Juana is coming tomorrow. [Indic.: verb of affirmation]
Preferimos que nos acompañes. We prefer that you accompany us. [Subj.: verb of influence]
Dudo que Miguel llegue a tiempo. I doubt that Miguel will arrive on time. [Subj .: verb of doubt]
Es una lástima que se hayan perdido. It's a shame that they got lost. [Subj.: impersonal expression of emotion]

Adverbial clauses give information such as “when”, “why”, “how” or “where” something happens. The verb in an adverbial clauses will be in the subjunctive if the action/state in the clause is anticipated —that is, viewed as being in the future in comparison to the action/state represented by the governing verb. The indicative is used in clauses where the action is viewed as habitual or having been completed.

Adverbial clauses are introduced by adverbial conjunctions, some of which by their very nature always indicate something anticipatory and hence always take the subjunctive:

antes de que (before)
para que (so that)
a fin de que (so that)
sin que (without)
a menos que (unless)
con tal de que (provided that)

Some of the more frequent adverbial conjunctions which may take either the indicative or the subjunctive:

cuando (when)
hasta que (until)
después de que (after)
tan pronto como (as soon as)
mientras (while)

Cada domingo después que desayunamos, la familia asiste a servicios religiosos.
Every Sunday after we eat breakfast, the family attends religious services. [Indic.: habitual action]

Cuando termines la tarea iremos al cine.
When you finish the homework, we'll go the movies. [Subj.: anticipated action]

Adjectival clauses describe or modify nouns or pronouns. If the noun or pronoun modified is negated, nonexistent or indefinite, then the verb in the modifying clause will be in the subjunctive; if the noun modified is a definite one, then the indicative is used.

Buscamos al criado que se llama Raúl.
We're looking for the servant who's named Raúl. [Indic.: definite antecedent]

Buscamos una criada que hable español.
We're looking for a servant who speaks [=might speak] Spanish. [Subj.: indefinite antecedent]

No necesito ningún amigo que me insulte así.
I don't need any friend who insults me like that. [Subj.: negated antecedent]

Como si is always followed by a past subjunctive, either the imperfect subjunctive (hypothesis in present time) or the past perfect (or pluperfect) subjunctive (past-time hypothesis).

Ella trabaja como si no hubiera otro día mañana.
She works as if there weren't any tomorrow. [Imperf subj.: present/future time]

Ella hablaba como si nadie la hubiera visto.
She talked as if no one had seen her. [Past perfect subj.: prior time]

“If” clauses. The indicative is used for both the “if” and “result” clauses if it is a “real” condition. In an “unreal” or “contrary-to-fact” condition, a past subjunctive is used in the “if” clause, and normally the conditional is used in the result clause. For present- or future-time unreal conditions, the imperfect subjunctive is used in the “if”clause and the conditional is used in the main clause; for past-time unreal conditions, the pastperfect subjunctive is used in the “if” clause, and the conditional perfect is used for the main clause.

Si ganas más dinero, iremos a Bogotá.
If you earn more money, we'll go to Bogota. [Indic.: real condition in present or future time]

Si ganaras más dinero, iríamos a Bogotá.
If you earned more money, we would go to Bogota. [Imperfect subj. & cond.: unreal condition in present or future time]

Si hubieras ganado más dinero, habríamos ido a Bogotá.
If you had earned more money, we would have gone to Bogota. [Past perfect subj. & cond. perfect: unreal condition in past time]

Note the tip-offs in English for unreal conditions in the above examples: the use of “would” or “would have” and the use of a past tense for a present/future time activity.

Reminders:
Tenses and forms: present subjunctive (hable, coma, viva = I speak/eat/live), present perfect subjunctive (haya hablado, haya comido, haya vivido = I have spoken/eaten/lived or I spoke/ate/lived), imperfect subjunctive (hablara, comiera, viviera = I spoke/ate/lived), past perfect (or pluperfect) subjunctive (hubiera hablado, hubiera comido, hubiera vivido = I had spoken/eaten/lived).

Sequence of tenses, or when to use which subjunctive:
If the governing verb is in the present, future, future perfect tense or is a command and if the subjunctive is required in a subordinate clause, use the present subjunctive for a simultaneous or future action or the present perfect subjunctive for a previous or already completed action. [Exceptions: 1) after ojalá when used as I wish and after como si use one of the two past subjunctives; 2) the imperfect subjunctive can be used after one of the “present time” tenses where the imperfect indicative would have been used if the indicative mood would have been used].

Dudo que vengan.
I doubt that they are coming/will come.

[The subjunctive is required after a verb of doubt; the governing verb is in the present tense. The present subjunctive is used for a simultaneous or future event.]

Dudo que hayan venido.
I doubt that they came/have come.

[The subjunctive is required after a verb of doubt; the governing verb is in the present tense. The present perfect subjunctive is used for a previous event.]

If the governing verb in a “past time” tense —imperfect, preterit, past perfect, conditional, or conditional perfect— and the subjunctive is required in a subordinate clause, use the imperfect subjunctive for a simultaneous or future action, or the past perfect subjunctive to indicate a previous activity.

Dudaba que vinieran.
I doubted that they were coming/would come.

[The subjunctive is required after a verb of doubt; the governing verb is in a past tense. The imperfect subjunctive is used for a simultaneous or future event.]

Dudaba que hubieran venido.
I doubted that they had come.

[The subjunctive is required after a verb of doubt; the governing verb is in a past tense. The past perfect subjunctive is used for a previous event.]