If you are new to the whole Omaha High game then think Texas Hold'em. It is very similar to Hold'em except with a few minor changes to the rules. The most obvious of these is the fact that you get a couple of extra hole cards. While in Hold'em you are dealt two before the flop in Omaha you are dealt four. There are other subtle rule differences but its very similar overall. There are lots of websites that host Omaha High games online (Bwin has a good selection).
To start you can head over to the 'Poke School' section to familiarise yourself with the concept. Everything is explained here in graphic detail so you can jump straight into a game after a couple of read throughs. Next download the poker game and you can get involved right away. There are lots of game rooms to choose from and regular tournaments that take place. On top of this they have lots of guides and helpful tips to get you started on the right foot whether its Omaha High or Holdem, you're covered. Next all you have to do is join a game - there's plenty of cash to be won... and lost!