I sit down and diagram everything out first thing. Usually, this means the base level rules as well as the 'Well, A can't go here or here because it's ahead of B and C...' stuff. That's key.
Grouping games are the hardest, and making a good diagram can be hard. Do the linear ones first.
I'm generally good at games in general, but I adore logic problems. I really do recommend doing those logic games puzzle magazines if you don't already. They're good for basic things and honestly? After doing the lsat, I'm doing the harder puzzles in those magazines without blinking. Not because the lsat is necessarily harder, but because the combination has gotten my logic skills better.
But the best advice really is just practice, practice and practice more. You might want to buy the Powerscore set-ups guide to help you out, if you're having trouble seeing how to lay them out. I also found that working through the LGB twice helped me a lot. The first time through, my score fell! When I didn't rush through the second I did much better. (And I was already good at them, just my score fell.)