Qualifications
While the creative part of Hollywood wants to know who you worked with, which mentors you had, what your dreams are made of, etc., the business side of Hollywood just wants to know that you can get the job done. If you can walk into any given film festival and walk out with five different producers having paid you upfront to help them sell their movie, then you really don't need anything except a good accountant.
Typically though, you'll at least need to have a solid base to start from, and that means showing up at as many events as possible―you have to be really, really visible.
Getting a position with a major distributor will definitely improve your power, fame, salary, and everything else we've written about, but it's going to require the most qualifications ahead of time (source). A bachelor's degree in something like communications, new media, or business management is a good idea, as is an internship or assistant position within distribution somewhere.
Then there's always the option of working your way up in a company, which can happen to anyone who shows the right initiative (although you'll be spending a good number of years being someone's gopher).
There is a gaping back door into this career: knowing the right people. If your daddy was a film distributor, and your aunt is a film producer, and your best friend in high school has a last name like Eisner or Lucas, then you've already got a leg up. Larger distribution offices will often overlook your lack of any conceivable abilities if you have the right name. After all, how much damage could one spoiled...er...special kid do?
Spoiler alert: all of the damage.