Ok, me and my best friend started the anime club at my highschool a few years back. Here's what I learned in my short time...
1. Watching anime is good. Watch plenty of anime. Try to get togeather on the weekends and have anime days. Don't watch anime every day at school though. You won't get much done as a club and it becomes more of a bunch of friends getting togeather to watch anime.
2. Try to do things like manga contests. Have a contest every once in a while like drawing a short 3-4 page short story. It is fun, competition helps as long as it's friendly, and it helps you learn who in your club can draw and thing up good story ideas. This helps down the road if you want to make things like shirts, or logo's for a web site. Also make little posters to help advertise on the club rally days.
3. Try to make sure you have a president, vise president, treasurer, librarian, and maybe even a rep for advertising and such. This helps out a lot by splitting up the responsibillity. Also, you won't be at the school forever, if you want it to keep going later, do vote ins for pres. and vise pres every year. If you do everything right, you'll get it next year, don't worry. That also helps keep confidence in you with the fellow club members.
4. Try to have donations and fundraisers. This helps build up the club account, though you may already have a budget, and let's you do things like go to a convention every year.
5. Vote on what anime's you want to watch and try to have everybody pitch in. You can buy a whole series and the club can watch it. People can also donate anime to help.
That's all I can think of for now. If I think of some more I'll post it. Those are the main points I wanted to throw out.
Oh and have fun with it. It's an anime club!