Youtube has a lot of calling clips that can give you an idea of how a contest is ran. You can go watch a contest or two to see how it works.
My advice would be to watch a few youtube videos and practice, then find a contest with an Amateur/hunter division and compete. Those divisions usually have lower entry fees and still can have nice prizes. That's how I got started.
Scott Ellis has a DVD called Mouth Call Magic that is about calling. I bought it, but have not watched it yet.
Good luck!!