Jazz drumming is all about the beat. It is very lively and requires use of every piece of the set. The best way to start off a jazz song is to get beat going by simply doing 1-2, 1-2 hits on the bass drum. From there you being to throw in other pieces of the set and have the song going.
Watch the video below for a guide to the basics of jazz drumming:

To seee Jazz first hand check out:
Blue Note New York
131 West 3rd Street
New York, NY 10012