The simple past tense, or preterite, is a verb tense that describes the past. In German it is more frequently used in the written form than in spoken language. For example, you'll see it used often in newspaper articles and novels.

Examples:
Professor Zweistein lebte und studierte in Heidelberg.
Das Studium beendete er mit den besten Noten.
Schon als Kind las Zweistein alle Bücher über schwarze Löcher.
Er schrieb seine Doktorarbeit über das Experiment.

Regular verbs in the simple past tense
For regular verbs, the simple past is formed by adding "te" and the personal ending to the end of the verb stem. When the verb stem ends with d or t, then "ete" is added.

Verb stem + -(e)te + personal ending

Irregular verbs in the simple past tense
For irregular verbs, the stem form changes in the simple past tense. Usually there is just a vowel change, but sometimes one or more consonants can change too. They are conjugated according to the personal forms but don't take the (e)te ending.

You've already learned the simple past forms of "sein" and "haben".

Some German verbs are mixed and have elements of both irregular and regular verbs. Like irregular verbs, their verb stem changes - but they also follow the conjugation pattern of regular verbs with the (e)te endings.

Note that in the simple past tense, the 1st and 3rd person singular do not take a personal ending.