Finite math at my school was mainly proofs on number systems. We used early axioms and kept building up the whole semester. It was alot like Geometry from high school.
Questions would be something like: Using only certain axioms, prove 0 * x = 0.
There was also prove different number systems were certain types. We worked with series quite a bit when doing induction proofs. The actual math isn't all that hard, but figuring it out and actually getting the proofs up to par was a challenge. Not the hardest thing ever, but frustrating at times.
Might want to find a class syllabus or book to see what kinds of stuff you'll cover. Wouldn't hurt to research the class for an hour or two at the bookstore (if you're using a book...we used some course packet the department had written up a couple years back).
EDIT: You know, come to think of it, I was talking about a Finite Math class but remembered that they also called the fresh out of high school not ready for Calc class some kind of finite math. It was mainly doing interest problems and real world kind of stuff like that. The Finite Math I took was taken after Calc I, II, and III.