The past tense suffix has four instances: -dı, -di, -du, -dü. How should we decide which one to pick? The answer is very simple. We look to the last vowel.

1. a or ı is followed by -dı,

2. e or i is followed by -di,

3. o or u is followed by -du,

4. ö or ü is followed by -dü.

Example:

"oku" (read) is the verb stem. The last vowel in "oku" is "u". Therefore we pick "-du" and it becomes "okudu"(s/he read).

Notice that when we use negative in past tense, the negative suffix -me or -ma comes before the past tense suffix and it will change the last vowel. 

Example:

okumadı (s/he didn´t read)

Of course the negative suffix itself follows vowel harmony as well.

Complete these sentences using the same verb once in affirmative and once in negative form in the same sentence:

Example:

(okumak) Ali çok kitap okudu ama Ayşe okumadı.