Some suggestions from a student applying for Law School from Mathematics
Informal Advice
This advice was kindly provided by a Mathematics student (successfully) applying to UBC Law school in the 2011 cycle. While very thoughfully prepared by the student, you should of course read carefully the Law School application information for the school you are applying to.

1) Start thinking about it early. One of the biggest mistakes you can do is try to cram for the LSAT or for the actual application. If you are thinking about purchasing study books or other materials you may need to wait a while for shipping if that is applicable - you need to factor that time in. You also need to register promptly for the LSAT otherwise you might end up writing it somewhere extremely inconvenient. You should be working on your personal statement for at least a month, and each school deserves a personalized personal statement that outlines details. Most people that I have asked have studied seriously for a minimum of 3 months.

2) As a math student you should have better developed the type of reasoning that is tested in the Analytic Reasoning and Logical Reasoning sections of the LSAT, which compromise exactly 75% of the scored sections. However, having a better disposition to do well is no excuse for not studying the material thoroughly. Continue to study for all sections, even the ones you are good at, because the LSAT can always throw a very difficult section at you.

3) Learn the test material however you want, either through self study, buying study books, or taking a course (I personally do not recommend courses to anyone), but the best way to continue studying after you finish learning the technical aspects of the LSAT is to do as many practice tests as you can. Take as many of them timed as possible, and make them somewhat stressful if possible, you want to simulate test day. For reference I did 25 practice tests in total, the majority of which were in the last 2 weeks before the LSAT - which I would not recommend doing this. Again you need to budget the time to do all these tests.

4) Go online and read all the tips on what to write for your personal statement and such. Realize that the majority of students will be following that advice without a second thought, so now you will know how to make your personal statement stand out from the rest.

5) Never practice on questions besides real LSAT questions. Once you are far along in your studies you will be able to immediately distinguish LSAT questions and those written to sound like LSAT. They are significantly different.

6) If studying for more than one test, such as LSAT, MCAT, GMAT, GRE, ASA (actuarial), etc. You have to budget your time even better. I have never been in this situation but from what I have read it is best to study for each test one at a time. So if you are writing two tests, they should not be written close to each other.

7) Some schools take the best score, while others look at the average. Plan accordingly in either scenario.