Don't know much about it, but a way to get started is to start working for free with independent mod developers.

Yeah definitely go around to different video game mod communities. The 2 engines I know of with a large mod community are the source engine (Although, it's kinda old now, so any projects would probably be done with by now), and the unreal engine. Just do a google search for Unreal engine 3 mods, and take a look around at projects that you would find interesting. Come up with some tunes that you think would be good, and submit it. If they like it, they'll put it in, and give you a credit.

Good luck!

Well, here's an excellent place to start: http://audiogang.org/
G.A.N.G. has lots of on-line resources and information about game composing in the form of articles, forums, and events. Also, here's an interview with Tommy Tallarico, founder of GANG, that provides lots of useful information: http://www.dperry.com/archives/interviews/interview_with_8/

Gamasutra.com (http://www.gamasutra.com/) is also a huge central hub of information on the game industry. You can dig pretty deep in that site for information on audio and composing in the game industry.

Aaron Marks has written an excellent book on audio (music and sound effects) for games, which covers not only the technical details but lots of insights and tips about working in the business. I'd highly recommend it. It can be found here: http://www.amazon.com/dp/0240810740/?tag=r06fa-20

If you want to start working on unpaid projects (mostly) to get your feet wet, make use of the forums at IndieGamer.com, DevMaster.net, and GameDev.net. There are plenty of projects needing music.

There are many more on-line resources, but these should help you get started.