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LSAT Analytical Reasoning---how to prepare

The LSAT is unique among the various standardized tests in that it includes sections that try to show the logic capabilities of the test-takers, based on logically analyzing reading passages AND doing "logic puzzles".  You may have seen logic puzzles in various media, such as Dell(tm) puzzle books or Games(tm) Magazine.   A typical puzzle would be on the lines of "Mrs. Wiggins has a case with four shelves, each holding a different animal toy that she got from four different relatives in four different years.  From the clues determine which shelves have which animal, who gave her the animal, and the year she got it."  There are then clues such as "The cat is on the shelf below the one she got from her nephew and above the one she got in 2011 (which is not the dog)."  With those clues, the solution can be worked out.  The difference between these puzzles and the LSAT is that these puzzles have one and only one solution, while the LSAT sets up situations then would ask "if the cat is on the second shelf, which of these five orders of the animals cannot be true?", then in another question would ask "if the one she got in 2010 is on the top shelf, which if these cannot be true?".   While this is a significant difference between the standard logical puzzles and the LSAT, there ARE some similarities in how to approach tackling the problems.  These include:
1.  Read the problem carefully, as clues may show up in the introductory material as well as in the listed clues (such as stating what the last item in a category is that isn't mentioned in the clues---in the above example including after the "four animals" a parenthetical (one of the animals is a deer). 
2.  Draw a picture of the set-up---in this example, draw four shelves and note what is over or under something else. 
3.  The elimination tables that are often included with puzzles may be helpful---drawing such for an LSAT problem may also be helpful.  
4.  In the LSAT as well as the puzzles, if a table is not provided, going through to note what are the items in the various categories is very useful (so getting down that the four animals are a cat, a dog, a deer, and a rabbit, the four relatives are a nephew, a niece, a son, and a daughter, and the years are 2009, 2010, 2011, and 2012).  
5.  Doing more puzzles for practice makes you better at solving.
6.  An important thing to take advantage of with the LSAT is that the test is multiple choice.  That means you can always work backwards by determining which answers are contradicted in some way, and so eliminate answers.  If you can even get it down to two, you've greatly increased your odds of guessing correavctly.  Remember with the LSAT that you can mark up the test booklet as much as you wish, so go for it.
While the above tips can help you, you might want to have tutor help to get you going and see problem approaches.  In that case, we who are LSAT tutors with Wyzant stand ready to help you out!
Good luck with the LSAT!