I'm a new member also (long time lurker, though).
Got this strategy from another forum. I've used it myself and it works:
1. Get the Powerscore Logic Games Bible. Go through it slowly. Do all of the exercises and make sure you understand all the major points before moving on.
2. Make three copies of every game you can get your hands on. Group these games by type (lsatblog.blogspot.com has this done for you online).
3. Start with Basic Linear games then eventually move on to more advanced games as you get better. Make sure to space out the games you work on so that you're not doing the same ones within 24-36 hours of each other. Focus on one type of game then move on (don't forget to still practice game types you've done in the past though).
4. After you do a game, review it. Make sure you're diagramming the rules properly and efficiently. And make sure you're seeing the necessary inferences necessary to answer the questions. If you don't understand something, don't just move on. Make sure you understand why every answer is correct.
Games was by far my worst section when I started studying for the LSAT. A normal section would be between -10 and -15 wrong. I'm now down to -2/-4 on any given games section by using the method above. Repetition is the key.