Testing the Waters
Another excellent way to gain experience is through an internship. That's right, you'd be surprised at how many game companies offer internships. They don't advertise them, they don't pay well, and they may require that you already live nearby, but they do exist. Lots of them. Visit the web sites of your favorite studios, and send out some inquiries. Many company sites have an easy to find "Jobs" or "Employment" link off the main page, but if not you can usually find it under "Corporate." There should be a generic human resources (HR) e-mail address somewhere that you can write to.
Now I'm going to give you what could be the most important advice I have to give:
You will be ignored. Do not give up.
I don't mean you're going to get an auto-reply rejection letter. You aren't going to hear anything, at all, from most of the companies you write to. You'll start to wonder if your e-mail is even working. It may be as bad as only receiving one reply out of a hundred e-mails, and that one will probably be a rejection. Doesn't seem very professional, does it? Well, that's just how it goes. Don't let it get to you. They just don't know you yet. Keep trying, and you will find someone who's interested.