Reversi is an interesting game. Those of you who havent played it could play it at Yahoo.
What almost gaurantees a win in Reversi is control of the corners. Therefore the main thing in Reversi is not to allow your opponent control of the corners.
One way to ensure that you capture the corners is to keep as few coins as possible in the beginning. If you have too many coins they restrict your play. With fewer coins you gain control of the game and can force your opponent to give you the corners. Once you have captured these you can reverse an incredibly large number of coins in the final few moves of the game to gaurantee yourself a victory.