Subjunctive: Present

Regular Conjugation:

Add an er/ir ending to ar verbs, and add an ar ending to er/ir verbs. Just switch them.

Important to know: 

Morir and Dormir, in their nosotros and vosotros forms, go from o → u, instead of o →ue. So the conjugations are durmamos and muramos

Irregular Conjugation:

Go verbs:

caer  caiga
decir → diga

hacerhaga
oíroiga
poner→ponga
salir→salga
tener→tenga
traer→traiga
venir→venga

 

Other irregular yo verbs

caberquepa
conocer
conozca
nacer
nazca
parecerparezca
construirconstruya
destruirdestruya
 

Dar/Estar

Dar: Dé, des, , demos, deis, den

Estar: Esté, estés, esté, estemos, estéis, estén

The words are bolded if they have an irregular accent.

Spelling Changes in the Subjunctive

c → qu: Buscamos → busquemos

g→gu:  Jugamos → Juguemos

z→c: Comienza → comience

g → j: Escoge → Escoja

gu → g: Siguen → Sigan

c → z: Convence → Convenza

Subjunctive with Noun Clauses

A noun clause is a clause that functions as a noun. So, you could say "I want a burrito" (Quiero un burrito), or you could say "I want you to give me a burrito" (Quiero que me des un burrito). The latter clause of the second sentence functions as the noun. Noun clauses that are incorportaed intoa  longer sentence are called "dependent" clauses, and they are introduced in Spanish with the word que.

The following expressions are indicative:
Saber: Sabes que lo hizo Sandra. You know that Sandra did it.

Parecer: Nos parece que está lloviendo (We think it's raining). Remember, parecer is like gustar, so it's NOT nos parecemos.

Oír: He oído que hay una buena noticia. I've heard there's good news.

Ver: Veo que Juan no entiende. I see that Juan doesn't understand.

Subjunctive is used when the dependent noun clause is not part of reality or of the subject's experience. They express expectation, skepticism, doubt, uncertainty; demands wants, needs, insistence, advice, impositions of will; negated facts.

Subjunctive:

Dudo que Uds. lleguen para las tres. I doubt you'll arrive by three.

Paual quiere que la visites. Paual wants you to visit her.

No es cierto que nos quedemos. It's not certain that we'll stay.

Other verbs that cause subjunctive:
Desear, esperar, insistir en, necesitar, preferir, querer

In order for a sentence to have a subjunctive clause, it must be expressing something about another person. If you express a wish about yourself, you just add the infinitive. For example, "I want to leave" would be "Quiero irme". To say, "I want him to leave", you would say "Quiero que se vaya." 

Decir and Pedir can be used as subjunctive too, when you're telling or asking someone something. Decir can also be indicative if you're describing what someone said. 

Demands, wants, needs, and desires

Aconsejar, exigir, impedir, mandar, permitir, prohibir, recomendar, rogar, and sugerir are all subjunctive.

Dejar can be followed by a subjunctive noun clause, or simply the infinitive, with NO CHANGE in the meaning. 

Emotional State

Alegrarse (de) , extrañar, gustar, sentir, sorprender, temer, and tener miedo (de) are all subjunctive.

Subjunctive with Impersonal Expressions

Many impersonal expressions are subjunctive. For example es necesario que, es importante que, es imposible que, es improbable que, es posible que, es preciso que, es probably que, and Ojalá que are all subjunctive. 

Ojalá que means "God willing", and it comes from Arabic "wa-sa allah" ("and may God will it").

Maybe, Perhaps

There are three major expressions for maybe, or perhaps. Clearly, they should be subjunctive because they express uncertainty, but one of those expressions is an exception. 

Tal vez: Perhaps, maybe subjunctive

Quizás: Perhaps, maybe subjunctive

A lo mejor: Perhaps, maybe INDICATIVE.

I'm not sure why, but that's something you have to memorize. 

Emotion

Es bueno que, es (in)útil que (useless/useful that), es malo que, es mejor que, es peor que, es triste que, es útil que, and más vale que are always subjunctive.

Es una lastima que can be followed by subjunctive or indicative, but most of the time it's subjunctive. 

Negative

No es cierto que, no es evidente que, no es obvio que, no es que, no es/está seguro, no es verdad que, no creer que, and no pensar que are always subjunctive. If they weren't negated, all of them would be followed by indicative.  
 

**Sometimes no creer que, no pensar que, quizás, and tal vez can be followed by indicative. That indicates a greater degree of certainty. The use of subjunctive in that case is still correct.

Doubt

Doubt is always subjunctive. Dudo que and es dudoso que are always subjunctive. If you negate those, so no dudo que, and no es dudoso que, they're indicative expressions. 

Subjunctive with Adverb Clauses

Always subjunctive

En caso de que- (In case)
Example: Yo traje mi dinero en caso de que mis amigos no lo trajeran. (didn't return on time)

Sin que (without)
Example: Nosotros hacemos la tarea sin que Haron ayude. (We're doing the homework without Haron helping)

Con tal de que (Provided that) and A menos que (unless)
This is kinda different; If the adverb clause is in the past, yo must use the present perfect subjunctive (haya + __)
Yo estudio inglés con tal de que mi maestra me enseñe.
Yo estudié inglés con tal de que mi maestra me haya enseñado. 

Para que (for)
Yo lo hago para que mi madre esté orgulloso de mi. (I do that so my mom will be proud of me).

A fin de que (so that)
Yo hago mi tarea a fin de conseguir una nota alta. (note the use of the infinitive, because the subject (I) stayed the same in the adverb and dependent clauses). 

-David Witten