As jhuskey said, you'll need a specific track bike to ride on most velodromes. Some, mostly likely outdoor concrete ones, will allow you to ride a road bike during closed sessions but for safety reasons you'll never have road bikes and track bikes mixed.
Renting a bike is a good way to start. Maydog did the right thing. Take a beginners course on how to ride track and take things from there. That course will likely be cheaper than trashing a pair of shorts when you go around the banking too slow the first time and slide down past the datum line in a rather unceremonious manner.
Ride, learn, have fun and expect it too be very, very painful.