Oh, well.
First off, you ned to read the rules you just need to read the "Challengers" and the "Gym Leaders, E4 Members, Challengers" section.
Then, you just take a look what gym you would like to challenge.
If you have chosen one, then read the rules under the banner of the gym you`ve chosen.
Finally, you post your challenge in the thread and send a VM to the gym leader (clicking on the banner links you to the gym leaders profile).
Got it? ;) Or do you still have some questions?