Hi Lamby, click on the 'tournament' link above, then on the backgammon link. It will say 'sign up for this tournament', or something along those lines!
You need 7 empty slots, and you can only play in one tournament at a time.
Goonerg is offering a prize tourney where you can win 6 month knight membership! Then you could enter more than one tournament if you had membership!! (Not that I'm trying to put you off the backgammon, EVERYONE is welcome! Just thought I'd point out the better offer in fairness!)
Good luck and I hope you can join in! I'll probably be doing another one after this if it goes well.