Qualifications
If you're willing to do manual labor for not much pay to get your foot in the door, you'll have a lot of leeway with your opening qualifications. There are certainly no degree requirements or expected courses, but you'll definitely have to demonstrate your worth—especially if it's on the more technical side like working the sound board.
In a lot of ways, being a roadie is a sink-or-swim kind of job: if you can do the job, great; if not, you'll have to enjoy the show from the audience (or not at all).
To make a career of being a roadie make sure you listen, follow directions well, and learn how to do things like rig cables and lights. If you're stuck as the low roadie on the tour bus, lugging equipment or making sure the artists have their Starbucks in the morning, you need to make yourself more valuable by adding to your skillsets.
All that said, there are some certain attributes that would make it easier to get the gig. Be dependable, and show up on time ready to work. It also helps to be easygoing, and it's certainly a good idea to look to tour with a band whose music you actually like.