There are many different variants of the Mahjong game that it can be tough to learn. The two prevalent versions, at least where I live, are the Hong Kong and Taiwanese styles. They have the same basic rules, but minor changes to the calculation of points (Fan) results in completely different strategy and play style.
I've played the game online a couple of times (I can't recall the site), but the problem is people are damned slow online, which completely disrupts the flow of the game. Playing it for real is so much more fun, you just need 3 people to also know how to play.