What's the best way to study for an art history final?

If you have notes on the certain periods, with examples of the works, go online or in your book and memorize what each painting looks like. For instance, if you are study da vinci and your teacher has talked about the last supper, go to your book or online and look at the painting for a while so you an answer questions about it. That should also help you tell each painter apart from the other

Yes you need to examine the styles. I don't know to what depth your teacher has taken you, but the other aspect may be comparing styles of different eras and painters. Best

I would focus on class notes, artists, and titles. I would also make sure I understand what the paintings were about on a literal level as well as what events surrounded the painting (any important events, why the piece was commissioned, etc.) and finally what links you might be able to make between different art works you have studied in that unit or during the course.

Good luck!