http://www.usgo.org/resources/howtd.html
when I was younger I used to hold quite a lot of LAN parties (with PC's ) with about 6-20 people each time. basically if you want to have a tournament you need to have a game that everyone wants to play. then you need to work out what sort of tournament there are some examples the link above with their descriptions.
you will need to know who is going to compete so you can draw up the roster we always played knock out tournaments mainly in FPS deathmatch. but did have a few stints at racing games where we had a points system based on where you finished in the race... for the wii personally i would with a Mario kart tournament as its new and infinitely fun depending on how many people want to play you can decide if you want to do a straight knock out, best of 3 knock out or a points based league.