There really aren't any "tricks" to Logic Games (nor are there tricks to any LSAT questions). The Logic Games, and the LSAT as a whole, tests logical principles. The more you know and understand those principles, the more likely you will do well on the exam.
As for Logic Games, specifically, here are two tips that should help you:
1) The most critical thing you need to do is diagram the rules provided and then use those diagrams to map out the different scenarios in the questions and answers. Proceeding through these games visually is the best and most effective way to do well on this section.
2) It's not what you know (or what's provided), but WHAT YOU CAN FIND OUT. By this, I mean that you can often take some of the rules provided (S comes before N) (N comes before G) and combine them (i.e., S comes before G) to reach new rules. The more effectively you can do that when you initially diagram the game, the quicker you'll be able to answer the questions. If that's a "trick," then so be it. But it's really contingent on your ability to use deductive reasoning.
Hope that helps.