The gameBefore attending a tournament, its best if you know the general rules for playing a game of backgammon with the doubling cube. If you don't, then you can read them on Backgammon Galore, but the best way to learn is to play some games. You can play with someone who knows how to play, or play online somewhere (like Yahoo or Pogo). Playing online may even be better for learning because the online sites enforce the correct standard rules.
Beyond the basic rules, here are a few technicalities to remember for tournament play:
Match playThere are some additional things that you'll need to know if you've played games of backgammon, but have never played a match. Essentially, a match is played to a certain number of points, usually an odd number such as 5, 7, or 9. The first player to reach that number of points wins the match. Each game played is worth one point for a regular win, two points for a gammon (meaning the losing player did not get any pieces off of the board), and three points for a backgammon (meaning the losing player got no pieces off AND still has a piece in his opponent's home board or on the bar). The number of points won for the game is then multiplied by the number turned on the doubling cube.
EXAMPLE OF A 7 POINT MATCH:
Important note: In match play, you must follow the Crawford Rule, which states: if the leading player attains a match score one game short of victory, then the next game of the match is to be played without a doubling cube. This one game in which neither player may double is called the Crawford game. (Named for John R. Crawford.) This rule did not apply in the example above since neither player attained a score of exactly 6 points during the match.
Tournament playIf you know how to play a match, but have never played in a tournament, then there are a few more things to know. The tournament may be a single or double elimination bracket, or a round robin, or some other format. The director may choose the format just before the tournament depending on the number of players.
Entry fees will be collected before the tournament begins. After the director draws to pair players together, the matches can begin. When a match is finished, both players should report to the director, who will update the bracket. All brackets will be posted along with payout amounts for all players to see.
For even more information about tournaments, here is a great tournament overview provided by Backgammon by the Bay in Oakland, CA
And here are the official U.S. tournament rules from the Chicago Point site.