I think I'm confused. Being a chapter advisor (which sounds to me like what you mean) is an unpaid, part-time, volunteer position. Chapters often have, in addition to alumni advisors, a faculty member who serves as a faculty advisor. (As the names suggest, though, you probably need to be either an alumni or a faculty member.)
If you want to work full-time with students, you should probably check out
www.naspa.org and
www.myacpa.org. It's not a field you just walk into without any previous experience. Those who start in it straight out of school usually had extensive RA or similar experience; generally you need at least a masters degree in education. Private sector experience is likely not transferrable.
And hey, October is Careers in Student Affairs Month. (Really!)