I recognize that there are variations in how much clothing is worn across cultures, even today, and that covering certain parts of the body is necessary in some cultures while completely optional in others. But as a whole, humans wear clothes. And other primates don't.
Do we know when that transition happened?
You might want to ask this over at /r/AskAnthropology as it deals with pre-historic times.
I'm an archaeologist, I don't specialize in ancient humans (and human evolution), but I suspect that the first anatomically modern humans were wearing clothes. It may even be the case that homo erectus and other pre-modern humans wore clothes, I couldn't say. I do recall that the reason (theoretically) humans don't have thick fur is because we started wearing clothes.
I'm not a historian, but if you look up Genesis 3: 7-21 in the Bible it gives a pretty good explanation of the how.