How would I go about getting started as a voice actor/voiceover person in the computer entertainment/whatever industry? I know that "people who can make silly voices" are not what they're looking for but I've taken some theatrical classes and understand the basic theory of drama, I can do a whole bunch of character voices, and just about everyone I have ever had to explain an esoteric concept to has commented that I articulate things so well that I should be a narrator or something. Obviously it's a piece of cake to get ripped off in something like this, so what would be a reputable place to start, maybe go in and get told "Dude you suck, stick to programming."

Voice actors usually are trained professionals, e.g. they work as actors in the theatre, film or radio drama.

Well, the only way you're going to get started is if people can hear you.
Do you have a friend you is good at recording and audio work? You should put together a demo voice reel, 2-5 minutes of you auditioning a variety of voices. Make sure its top quality, this is your selling material. Then you'll be ready for the minor leagues. Keep your demo reel uploaded somewhere so that you can link someone to it at a moment's notice. Then make it known here and on other indie/hobby gamedev forums that you are available for voiceover work. Let your demo speak for you.

Hopefully, if you keep your eyes open enough and your name in peoples minds, then somebody will have you on their smaller-scale project, and thats about what you should hope for at this point:)

I believe there is a fairly common misconception floating around that voice acting is easier, to do and to break into, than "regular" acting. I feel reasonably confident saying this because I've tried getting into it myself. I wasn't successful, but neither was I highly motivated. I would, however, be happy to share what I've learned from the experience. If you seriously want to be a professional, reasonably well-paid voice actor, find a good voice coach. Raw talent helps, but it isn't going to get you very far on its own. Like so many businesses, if you want to make money, you're going to have to spend; a coach worth your time isn't going to be cheap. Additionally, finding one in the first place can be rather difficult, especially if you, like me, live a great distance from a reputable recording studio. Offhand, if I recall correctly, Chicago, Atlanta, and Los Angelas are good places to live if you're serious about this, but don't quote me on that. If you don't expect to be paid well (or at all) the road is considerably easier, but either way, the place to start is getting together the best quality demo you can, whether it's for trying to convince a coach you are worth thier time or for posting directly to a site like Voice123.com from where you can link to the forums here and hope to get a lucky break. This is all from my own experience, so take it or leave it, but I hope it helped. Good luck.