That's great to hear that you're interested in starting ICPC at your college! It's always good when a student is enthusiastic about the competition! =). For the longevity of the club at your college, you will likely want to find a faculty member who is enthusiastic about the contest as well (or at least enthusiastic to help you out). This will go a long way in getting things done--they can assist with room bookings, printing, etc., which makes life a lot easier.

For starting out, I would recommend doing the following:

1. Contact your Regional Contest Director -- North America is broken up into 11 regions, each with their own RCD. Your RCD will be able to provide you with information in regards to your local area. In particular, ask about other universities/colleges around you that compete. You can contact those coaches and see if they have any advice specific to your area (most coaches should be willing to help out--speaking from personal experience, I have helped 2 other local universities start up their programming club). Also, from my experience, high up members of the university community (i.e., the people who could give you money) are more likely to support something if a competing university is doing it as well (good ol' fashion rivalries).
2. ICPC provides a PDF (here) that explains the contest in a nice way -- this should be helpful in encouraging your university to get on board.
3. If you are pitching your idea to CS/math profs, it is likely a good idea to bring a couple sample problems (easy-ish ones) so that they can get a feel for it. Since you are in North America, I find the best explanation is that this contest is like the Putnam Examination except you are doing proof-by-example.
4. I would start out asking for support from your university first and then branch out to seek support elsewhere if they are unable/unwilling to. If they are unable/unwilling to support you financially, the university will likely have a liaison office which will be able to provide you with companies to communicate with.

Once you have gotten the behind-the-scenes stuff figured out, make sure that you keep your club active--meeting once a week is probably a good starting point to get everyone familiar with everything. Food is a great way to attract people out--see if you can find funding for food each week, and if you can't, see if you can get funding for at least drinks (Coke, juice, etc.) at the practices--it goes a long way.

Good luck! And most importantly, have fun! =)