Spanish has two past tenses: preterite and imperfect. 

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¿Cómo se forma el pretérito?

To conjugate regular -ar verbs in the preterite, simply drop the ending (-ar) and add one of the following:
-é
-aste
-ó
-amos
-asteis
-aron

To conjugate regular -er and -ir verbs in the preterite, simply drop the ending (-er or -ir) and add one of the following:
-í
-iste
-ió
-imos
-isteis
-ieron

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¿Cuándo se usa el pretérito?

Generally speaking, the preterite is used for actions in the past that are seen as completed.
It implies that the past action had a definite beginning and definite end.
Juan habló de la una hasta las dos.
Juan spoke from one until two o'clock.  (clearly stated beginning and end)

It is important to realize that the beginning and the end may not always be clearly stated.
Juan habló dos horas.
Juan spoke for two hours.  (implied beginning and end)

Juan habló con la estudiante.
Juan spoke with the student.  (implied beginning and end)

The preterite is used for actions that can be viewed as single events.
Ella caminó por el parque.
She walked through the park.
Ellos llegaron a las ocho.
They arrived at eight o'clock.

The preterite is used for actions that were repeated a specific number of times, or occurred during a specific period of time.
Ayer escribí tres cartas.
Yesterday I wrote three letters.

​Vivimos allí por cuatro años.
We lived there for four years.

The preterite is used for actions that were part of a chain of events.
Ella se levantó, se vistió, y salió de la casa.
She got up, dressed, and left the house.

The preterite is used to state the beginning or the end of an action.
Empezó a nevar a las ocho de la mañana.
It began to snow at eight in the morning.

The above examples all fall within our general rule for using the preterite: ​The preterite is used for past actions that are seen as completed.

Verbos irregulares en el pretérito

These four verbs are irregular; you must memorize them:
SER    IR    DAR    HACER

-ir verbs that change in the present change in the preterite, but in a different way: 
PREFERIR, DORMIR 

In order to preserve the sound of the infinitive, a number of verbs change spelling in the preterite tense.
The following changes occur in the "yo" form only:
Verbs that end in -gar change g to gu
Verbs that end in -car change c to qu
Verbs that end in -zar change z to c
Here are three examples:
yo jugué (jugar)
yo busqué (buscar)
yo almorcé (almorzar)
For verbs that end in -aer, -eer, -oír, and -oer, the él/ella/usted forms use the ending "yó" (rather than ió) and the third person plural uses the ending "yeron" (rather than ieron). The remaining forms gain a written accent over the letter "i."
creer
creí
creíste
creyó
creímos
creísteis
creyeron

Verbs that end in -uir change in the same way, but the written accent over the letter "i" only occurs in the yo form.
huir
huí
huiste
huyó
huimos
huisteis
huyeron
Other verbs like huir include:
construir
contribuir
destruir
fluir
incluir
influir

The following verbs are irregular in the preterite and must be memorized:
DECIR, TRAER, VER


A number of verbs that are irregular in the preterite follow a particular pattern. While their stems change, they all take the following endings:
-e
-iste
-o
-imos
-isteis
-ieron

Here are the verbs:
ANDAR, ESTAR, TENER, CABER, HABER, PODER, PONER, SABER, HACER, QUERER, VENIR

Modified from the original at StudySpanish.com.