Starting a paintball club at your High School or College requires just 2 things, a well written proposal and someone driven enough to hand it in and see things through.
If you are that person to hand it in, the only thing left for you to do is to write up a 10+ page proposal of what it is you intend to do with your paintball club. In this proposal you should convince your school WHY it is beneficial for them to sponsor a paintball club, and why it will be beneficial for students. It needs to be packed full with examples of successful clubs at other schools and needs to include just what it is you intend to do with the club. Things like accomplishments you hope to achieve, events you plan on running, and your budget needs to be covered. Perhaps one of the biggest things your school will be looking for in your proposal is how you intend on minimizing the liability and risk the school will be taking on by having your paintball club.
You should plan on taking a couple of weeks to prepare a quality proposal. There are a lot of paintball naysayers out there that will gladly throw it away if it isn't up to par. One of the best things you can do is hit up the College Paintball Association, they have loads of resources and information that will be helpful in writing your proposal. Both High School and College paintball information can be found there.
If you are looking for a great example of a proposal for starting a paintball club at a school, check out this one being sold on eBay (Start a Paintball Club). It costs about $7, which isn't a bad trade off considering all the research and structure has been done for you. If you want to get things going at your school as fast as possible, this is probably your best bet.
Just be sure whatever you do in starting a paintball club at your school, approach it in the most professional way possible. Your not just representing yourself, your representing the entire sport of paintball.