Andrew, that's the question of the century! There's so much to say about this that I don't think I can really do your question justice here. I'd start by reading the first couple of chapters our logic games strategy guide - (you can download those for free here:
http://www.atlaslsat.com/lsat-books.cfm) and then start learning strategies for each game type in the following chapters. After you learn the basics of a game type and how to diagram it, practice with some simpler games of that type, and then move on to examples that add in a curve ball (or two!). Then you work that into full preptests.
Our philosophy is to master the game types while remaining flexible. There's no way that one can prepare for every game, as the LSAT will always come up with new twists, so instead, get used to thinking on the fly.
I'm sorry I couldn't spell out more, but again, that's a huge topic, and I think you need to start by getting a book or self-study program (
http://www.atlaslsat.com/lsat-self-study.cfm)
Good luck!