The main division between past tenses in English is according to when the events happened in relation to the frame of discussion. In Turkish, however, the main division between the past tenses is according to the relationship of the teller to the information provided.
Something that is definitely known or which was seen at first-hand uses the ending -di (with appropriate vowel and consonant harmony):
Beren çarşıya gitti – Beren went to the market.
Dün okul bitti – Yesterday school finished.
Yazıyı sildim – I erased the writing.
Something that is second-hand, whose reliability may be questioned, or that was not known at the time and was learnt later, uses the ending -miş:
Beren çarşıya gitmiş – Beren apparently went/is said to have gone to the market.
Dün okul bitmiş – Yesterday school apparently/I believe finished.
Yazıyı silmişim – I apparently/later learnt that I erased the writing.
These past tenses can also be added to other tense suffixes:
So something that was happening repeatedly in the past uses -iyor + -du/-muş (-di/miş with vowel harmony):
Beren her Cuma çarşıya gidiyordu – Beren was going to the market every Friday (at that time).
Küçükken brokoli seviyormuşum – When I was little, I apparently/have heard that I used to like broccoli.
Something that was going to happen uses the future tense -ecek +di:
Dün okul bitecekti – Yesterday school was going to finish.
Beren çarşıya gidecekti – Beren was going to go to the market.
When talking about what would have happened if something had happened differently in the past, you use -se +(y)di/(y)miş and for the consequences we use +(e)r +di or +ecek +di:
Beren çarşıya gitseydi, evde ekmek olurdu – If Beren had gone to the market, there would be bread at home.
Dün okul bitseydi bugün plaja giderdik – If school had finished yesterday, we would have gone to the beach today.
Yazıyı silmeseymişim iyi olurmuş – If I hadn’t erased the writing, (I’m told) it would have been good (i.e. I’m told it would have been good I hadn’t erased the writing).
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