The above suggestions are very good for getting started. Get involved on some forums. There are game developers looking for composers who will work for free. This is a way you might be able to get a few credits and build some relationships.
Try and make as many connections as possible. Have any friends going into video game development? How about a relative or friend who knows somebody? I've been doing work as a film composer for about two years now.
Not with much success but very enjoyable and gratifying when you work on a good project with good people. I might offer the advice that you need to be very determined in this field and always push for more. Connections aren't easy to make and actual compensation is even more difficult to come by. Also, don't be afraid of rejection. Don't let me discourage you though. These are just my experiences.
I almost forgot to mention that if you plan on doing independent work, you better be good at using a DAW platform. ie. Pro Tools, Logic, Nuendo, Digital Performer, etc. The overbearing majority works this way. Maybe 1% of video game composers actually write the score and have an orchestra perform it with a hired audio engineer. And even that 1% probably works on the computer to make "Mock-up's" (digital emulations of a score).
Here's a forum that is a little more focused on composing for media. http://www.vi-control.net/forum/index.php
Here's a kinda crappy "how to become a video game composer" article. But might have something you'll find useful. http://www.ehow.com/how_6177769_become-video-game-music-composer.html
Good luck! Your hard work will pay off. Learn as much as you can and remember to smile even if things aren't going your way! Eric
