I was a founder of my fraternity in college. Not exactly like starting a new organization from scratch, but probably similar to starting a branch of a national organization. There are a lot of pitfalls and difficulties.
The initial members may not have the same vision for the group. For our group, 60% dropped out within the first few months. Which leads to the second point, recruiting will be critically important to maintaining the groups presence on campus. A lot of rules govern fraternity recruiting at most schools, but you won't have to deal with those. Typical recruiting events include social events, mixers with other campus groups, charity/volunteer events, awareness events, sporting events and combinations thereof. For example, as a fraternity we had typical rush social events, but we also did awareness events like a "beeperball" hitting event (awareness for the blind) that tied into our national philanthropy. We got local restaurants to donate food and had people that walked by try to hit the beeperball. We made contact with a lot of perspective members this way. As a new group, you'll probably spend a lot of time manning a table at the campus square/walk/whatever, with other groups. You'll probably do a combination of these things depending on the focus of yoru group.
So, the process of getting a new group set up should be pretty basic; you'll just need to register with the school in some way. The effort required to get it off the ground is somehting else entirely. I directed recruitment at my fraternity the entire time I was there, and we recruited some 150 people over the course of the first two years to earn our charter with about 50 active members. To finally maintain our numbers I (and our treasurer) had to creatively negotiate a lease for a house for our chapter - a very difficult task that our national organization said couldn't be done in Westwood. Until your group is established on campus, people will come and go, and you will spend a lot of your efforts dealing with things you never expected to face.