Something like this would require a few steps. First, find a teacher who you like or who would be comfortable supervising (since that's usually a necessity). Mostly right now you want to give them intent and ask their interest. You may have to ask a few different teachers. If/when you find one, you have to put in a little more work.
Not necessarily in order:
- Evaluate/garner interest. Ask your friends, poll classrooms, hand out surveys or put up fliers. The faculty is going to want to know if there's actually merit to running this club. Recruit a close friend to help co-run or co-host tournaments/get-togethers. This will also include polling for an ideal time/date. There are lots of other clubs in any given school, and they'll run whenever they can. Find a timeslot you can work with, and that teachers can give you.
- Assess and acquire assets:
-- You said you can only confirm 2 setups, but if more than 20 people show up to play, that might not be sufficient, especially if you're gonna stick to a competitive environment with mostly two people to a setup. Check local ads and stores for cheap TVs/Gamecubes/Wiis/Whichever you need, leaning towards ease of transportation with TVs. You could even have a donation run. There may be lots of people willing to unload old CRTs on you, and that's the best thing ever for you.
-- You'll need a fairly large, fairly open room with a lot of plug-in availability. Tables and chairs will be necessary. Look into potential secure storage spaces that the school could offer you if students aren't willing to haul setups to and from school. If it's a decent trek through the school away, ask about carts you could use.
- Compile all your information and present it to the teacher you found, or to both the teacher and the principal. Be professional and serious about it, so you don't look like some kids looking to goof off. If you're hoping to start up a competitive environment, specify that. If there's going to be any money involved, note how much and who's going to take care of it. If you're leaning toward casual smashfests, consider a one-time membership fee that you can put towards the club (acquiring more setups, etc.), and if it's going to be competitive, run over how a bracket buy-in and pot splits will work. Outside of tournament winnings, no money taken in by the club should go anywhere except back to improving the club.
Look into all the TOing advice threads, as unless that's getting delegated, you will probably be running things moreso than you will be playing things.
That's about all I've got for now.