Know that in every Logic Game, the given rules and conditions will supply with enough (and sometimes more than enough) information to answer the questions. What makes them difficult however, is that many questions will hinge on a key deduction, a logical consequence of a combination of rules. Before you approach the questions, look for other inferences you can make based on rules.
Don't get hung up on trying to "solve" the games. The makers of the LSAT purposely set up some games so that the number of correct combinations of elements is unwieldy. In these Logic Games, the accompanying questions introduce new conditions to help you narrow down the possibilities.
Practice drawing diagrams for the main types of games: matching, sequencing, distribution, selection, and hybrid logic puzzles. If you cannot naturally come up with a diagramming system, get a Logic Games workbook, or consider taking a LSAT prep course. If you have a system, but it's not working for you, start from scratch and take a new approach to drawing figures.
Practice drawing logic diagrams neatly on the test page. This step may seem trivial, but you have to remember that during the LSAT, the only paper you can write on are the pages of the test booklet. The best way to keep all your Logic Games figures straight is to draw one "master blueprint" at the top of the page, and then smaller question-specific diagrams next to each problem. If you draw them haphazardly wherever there is space, you will confuse them!
Realize that some questions are designed so that you can use the answers from previous questions to help you rule out wrong answer choices.
Realize that the 4 games are not necessarily ordered from easiest to hardest in the LSAT exam booklet. Therefore, to maximize the number of questions you get right, start with the easiest game first, and do the hardest game last. In about 30 seconds, you can skim the 4 games to determine their difficulty levels.
Take timed quizzes. You have 35 minutes to complete 4 Logic Games, which works out to around 9 minutes per game. If you can do the easier sequencing games in about 7 minutes, you can buy more time for the more challenging distribution and hybrid games.