Serious game testers need to be able to test every aspect of a game. You have to spend hours finding ways to break a game, write reports about it, and be able to communicate some ideas of your experience to the developers. Having developers properly communicate with game testers is often the difference between a good game, and a great game. Just be aware that playing games for a living and finding bugs all day isn't as fun as playing a finished game for your own enjoyment.
Now then your best bet is to find local game developers. Go in, apply, bug them, buy them lunch once in a while, or at least a beer at the bar, and keep trying. It's easier to choose someone you know and trust than some random guy from the stack of applications they get. It's not a good paying job, and it's alot more work than you think. With great persistence, you could end up with it, but you have to really want it.