Before 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 the US Backgammon Federation site, 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:
Each player should roll on the side of the board to his/her right.
Dice should be rolled out of a cup.
A player's turn is not over until he/she picks up the dice (when each player uses a separate pair of dice) or taps the bar (when both players share a set of dice). Moving the dice out of the way to facilitate moving your pieces is fine, but you should first announce what numbers are showing so that there is no confusion.
Both dice must land on the playing surface or on a checker on the right side of the board for a roll to be considered valid. If either die lands off of the board, on the wrong side of the board, or lands cocked on its side against a checker or a wall of the board, then both dice need to be re-rolled.
There 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:
Game 1: Player A wins a gammon (player B got no pieces off), and the doubling cube was not turned during the game, so player A wins 2 points for the gammon.
Game 2: Player B offers the cube to player A during the game and player A accepts. Player B then wins a gammon win, worth two points. But since the cube is at 2, the game is worth 4 points (2 x 2).
Game 3: Player B offers the cube to player A, but player A refuses. Player B wins one point.
Game 4: Player A offers the cube to player B and player B accepts. Player B wins a normal win, and since the cube is at 2, the win is worth two points.
Player B wins the 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.
If 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, if any, would be collected before the tournament begins. After the director draws to pair players together, the matches can begin. When a match is finished, the winner should report to the director, who will update the bracket. All brackets will be posted for all players to see.
In general, rules will follow the standard USBGF tournament rules.