I started one way back in the day for AIDS awareness. Our school's orgs all have their own group in our online program called KnightVision (it's a customized Blackboard 7.0, if you school has that). Anything important at school somehow gets worked into the KV interface. In order to start a KV org, we have to have a "sponsoring" professor, so on our political science profs that teaches "Politics of AIDS in Africa" was our official faculty person.
After setting that up, I also had a listserv, which is an official school e-mail address that goes out to all the people in the organization.
We only ever did a few things though, because I discovered a lot was already being done by the Social Justice Committee, which is much larger and more well known, so I ended up handing them the materials I was using because they could reach more people.
I guess it depends on how your school's orgs go. I'd first contact Student Life or Student Development (whatever you call it) and see if there's not already an existing org. that needs help or needs to be reorganized. If you've got something really specific in mind, see if anyone on the social justice org (or whatever your equivalent is) would be willing to help, or make it like a "sister" project. But yeah, it all depends on protocol and where the money comes from. I'd try to do it "officially" so maybe the StuDev office can give you money for materials and events.