Don't play the American version if you can avoid it because the odds are worse. Study combination bets and never bet on single numbers. Watch the game for a while before you play and never bet more than you can afford to lose.
I don't know enough yet to be able to give others advice, but reading through this thread I got a lot of great tips for myself. I'm wondering about the advice from Muay, though. It sort of doesn't make sense to me. Care to elaborate a little more?