The subjunctive tense in spanish is used to express ideas for which the speaker knows or doubts exist in the real world. For example: I doubt John is coming today. The form of the subjunctive for regular -ar, -er, and -ir verbs is layed out here.

For the -ar verbs, using hablar as an example, the subjunctive endings are:
hable = I speak (subjunctive)
hables = you speak (subjunctive)
hable = you (form.) speak, he/she speaks (subjunctive)
habléis = we speak (subjunctive)
hablen = you (fam. pl.) speak (subjunctive)


For -er verbs, using comer as an example, the present subjunctive endings are:
coma = I eat (subjunctive)
comas = you eat (subjunctive)
coma = you (form.) eat, he/she eats (subjunctive)
comamos = we eat (subjunctive)
comáis = you (fam. pl.) eat (subjunctive)
coman = you (form. pl.)/they eat (subjunctive)

And finally for the -ir verbs, using vivir as an example, one can see that the subjunctive endings are identical to the -er verbs:
viva = I live (subjunctive)
vivas = you live (subjunctive)
viva = you (form.) live, he/she lives (subjunctive)
vivamos = we live (subjunctive)
viváis = you (fam. pl.) live (subjunctive)
vivan = you (form. pl.)/they live (subjunctive)

It will help to see the subjunctive at work in some short sentances.

For -ar and -er stem changing verbs, the stem change applies as usual, except there is no change in the nosotoros and vosotros forms. However, in -ir verbs having the stem-change o:ue, in the present subjunctive the o is changed to a u, and in those having an e:ie stem change, the e changes to an i.

Sometimes the present subjunctive forms of common verbs are irregular and must be memorized.

The formula to create the present subjunctive form for verbs irregular in yo, (which also works for regular verbs), starts with the first person present indicative. If the final -o is removed, what remains is the subjunctive stem, which can be used to create the conjunctive forms.

trato = tratar, first person present indicative
trat- = tratar, subjunctive stem
trata, tratas, trata, tratamos, tratáis, tratan

conozco = conocer, first persent present indicative
conozc- = conocer, subjunctive stem
conozca, conozcas, conozca, conozcamos, conozcáis, conozcan

Some conjunctions strongly indicate the subjunctive form will be required. If you use the conjunctions below, be prepared to use the subjunctive.

The conjunctions cuando, hasta que, tan pronto como, and en cuanto require the subjunctive when they are used to indicate the uncertain future, or in commands.

Here I'll simply list some examples that I found interesting of the subjunctive at work