"to be done with something" can mean to be no longer using it.
Are you done with that newspaper? May I have it?
Are you done with that screwdriver? Shall I put it back on the tool shelf?
"To be done with something" can also mean "to be ready to abandon or quit something" or "to have had enough of something (undesirable), to be ready to put an end to something"
I hate my job. I'm done with it. I'm going to give notice this Friday.
I'm done with your nonsense and your back-talk. You're grounded.
"To be done with" or "to be over and done with something" can also mean to have gotten through it, as an ordeal.
I am done with midterm exams.
I am over and done with finals.
I am over and done with anger management counseling.
I am over and done with physical therapy.
P.S. I am a speaker of AmE. "To have done with" in the sense of "to abandon, as something or someone that deserves to be abandoned", seems a BrE locution to me.
You are expected to have done with such bad study habits by the time
you reach university.