There are two ways of doing it:
1. Simply organise amongst yourselves (by sending private messages for example) who is going to play who, what the time settings are etc etc and then get people to challenge each other. There is a Challenge Cup that just started here between some of the clans that was done that way, and the person who organised it created his own webpage to keep track of the results.
2. If you want to do a tournament that's officially recognised as a tournament here on the site, then you would need to contact Russ (the main site administrator) and discuss it with him.