It really depends on the position you're looking at. As an example, I'm in Player Relations but I got started by volunteering for community fan sites almost 10 years ago. This gave me great experience in some of the "how" and "why" of community, and presented a lot of fabulous opportunities for me -- I was given the chance to meet developers, make some life-long friends, and really get my feet wet with content creation.
I worked as a volunteer for roughly 2.5 years before I was picked up by a studio (via the contacts I had made while volunteering) to do entry-level community work. I was in school for Interpersonal Communications at the time (Communications degrees are the way to go if you're looking to dive into Community work), but made the decision to drop out to pursue my career. The rest is history -- I bounced around a lot before finally arriving at Riot.
If you're looking to do game design, the best advice I've heard is to simply make games in level editors. A lot of great designers I've met began their journey with pencil and paper games, such as D&D, or board games. There are also a lot of great game design programs (and game programming) these days, but do your research on the school before registering.
Programming, art, and marketing all benefit from having a degree, but don't abandon real-life experience with whatever you want to do! Not only is creating something you're passionate about very rewarding, but it is also the best way to gain the kind of applicable skills that you'll need in game development.
GLHF!