When I took the LSAT in November 2003, I first read the first sentence of each paragraph, the entire first and last paragraphs and then the questions (not the answers). I then returned to the passage and read it fast in search of answers to the questions and when I found an answer, I marked it. I was able to only skim many sentences for key words.
I finished with over 10 minutes left to review my answers and missed one question. It worked for me, doesn't mean it'll work for anybody else.