First off, you need to know how to take the test. The games section and the logical reasoning sections only have about 6 or 7 types of questions. This is where a course comes in handy. If you know all the types of logic games, you can jump right into making the correct diagram for the game. The same thing goes with reasoning – you can throw out several answers right away if you know the question type. Most reasoning questions come down to only 2 choices, and the other 3 are easy to dismiss. Reading is the toughest, because you have to read fast. A course will teach you what to look for when reading and how to mark up the passage if you need to do that. I do recommend Kaplan if you can afford it, because they teach you how to diagram the logic games correctly. A lot of people do ok on the games section through innate talent, but they don’t do as well as people who know the games and diagrams inside and out, even if they are bad at logic puzzles. The logic games are where most people can get the biggest gains by practice and learning, but don’t get too focused on any one type of section. If you can’t afford Kaplan (which is overpriced) you might be able to get their books from craigslist, or take a class from your local college. Princeton is good too, but I don’t have as much experience with it.
Secondly, practice is important. I don’t think you should take entire tests at home, but do 3 or 4 sections each day, checking your answers after each one and figuring out what you did wrong. Do this for a month or two before the test.
The most critical aspect of the LSAT is time. When you practice at home, have a timer. I don’t recommend a watch, but a stopwatch or something will do. Short yourself 5 minutes on each section you practice on. Learn how long you have for each question, and use the time if you need it, but always be ready to move on to another Q and come back. There are no guessing penalties. The benefit to practicing with less time is that you will feel less stressed on the real test, and you will have ingrained the habit of moving fast.
You can buy real LSAT tests from all kinds of places. LSAC sells them, Amazon has them, etc. Buy lots of these so that you can practice, practice, practice. Books with explanations are good.
So, in short: A course teaches you HOW to take the test, then you need to practice seriously, with shortened time limits, so that you can do diagrams and such automatically. Expecially in the higher scores (168 and up), one or two questions will change your score, so moving from a 168 to a 169 is a matter of getting only two additional questions right.
Notes on getting in to school:
The LSAT is the biggest factor in the school you get into. It is also the easiest factor to influence. Anyone can make a 10-15 point gain with the right kind of practice and seriousness. That is a HUGE difference in schools – literally 100 or more ranks. And yes, going to the best ranked law school you can is deadly important, if only because of employment contacts. So take the LSAT with as much seriousness as you can muster, because it is incredibly important.