How do you form an aorist verb?

In Ancient Greek, the aorist is the equivalent to our simple past. There are two forms of aorists: the sigmatic first aorist and the thematic second aorist.

The sigmatic first aorist is formed on the 3rd principle part. There is no trick to these, you simply have to learn them. Once you've got the principal part in question you must augment it. This is crucial, as the augment is the sign of the past tense (hence it is absent from the aorist infinitive and imperative). An augment is usually an epsilon (ε) but if the verb stem already begins with one you must lengthen it to an eta (η). If the stem begins with any other vowel simple lengthen it. Finally, to the end of the augmented stem, add a sigma (σ) follwed by the 1st aorist endings:

-α, -ας, -εv, -αμεv, -ατε, -αv (note that these are the active endings)

The thematic second aorist is the more common form of the two. Just like the first, it is formed on the augmented 3rd principal part. There is no sigma added for these, simply add the second aorist endings to the end of the stem:

-ov, -ες, -εv, -oμεv, -ετε, -ov (again, these are the active endings)