If you are talking about putting something on yourself, then only "put it on" is correct. You cannot use "put on it" for yourself, only if you are talking about things on top of other things. For example: A: Did you put on your jacket? B: I put it on! A: I put berries on my yogurt, but what did you put on it? B: I also put berries on it! In short, "put it on" is used for putting things on yourself such as clothes, hats, shoes, etc. "Put on it" is used for putting one thing on top of another thing, like putting a book on a table or putting berries on the yogurt.