I usually say I finished my class, and my friend told me he says I'm done my class. Is it proper or not? Your friend is only partially correct. "I finished my class" is correct if you have recently finished and you're telling your friend that you're now free to do other things. If you want to use "done", then you'd only use it if you have several classes, and you'd say, "I'm done with my classes (for today)".

I've just finished my lesson (or classes).

I finished my class

I'm done with classes for today... is fine... but informal.

It also depends when you are talking. If you meet your friend about five minutes after class, you'll say, "I've just finished my class." You then use the present perfect. If you talk later in the evening, you may say, "I finished the class early and then went for coffee." You then use the past tense.