Card tournaments are fun ways to spread awareness of a given card game, create healthy places for great players to compete and even raise a little money for yourself or a given charity. Much of the work surrounding card-game tournaments stems from finding a venue, getting people to sign up and advertising your tournament so that spectators are aware of it. Once you do that, however, you need to organize the tournament itself in order to winnow through the competitors and find a champion.
Determine how long it takes to play an average game and how many competitors you have. Compare those numbers against the time you have to run the tournament. They'll have a huge impact on the format you use. You don't want to run over and you need your tournament to move along in a timely fashion.
Consider a single-round elimination format if you have a small number of competitors and/or a large amount of time. In this format, competitors are paired randomly against each other in one-on-one competition. The winners move on to the next round while the losers are eliminated. The process continues until only one player is left, making him the champion. If you don't have an appropriate number of players (eight, 16, 32, 64 or 128), then some players may need to receive byes during the first round in order to create an even number.
Use a double-elimination format. This is similar to a single-elimination format, except that players aren't dropped from the tournament until they have two losses. After the first round, divide the tournament into an "all wins" half and a "one loss" half. Continue playing until you have one one-loss player and one zero-losses player, who then play for the championship. The one-loss player must defeat the no-loss player twice in order to win. As with single elimination, this works best with comparatively small numbers of competitors.
Plan for a Swiss-style format if you have a large or uneven number of players. Within this format, all players participate in multiple rounds of competition, starting against randomly chosen opponents. They build up a record as they play (e.g., five wins and no losses, two wins and three losses) which provides for an easy ranking system. Set those with identical records to play against each other, providing parity as the competition continues. When the Swiss rounds are over, you can either select the top-ranked player as the winner, or select the top-eight or top-four competitors for single-elimination play-off rounds. They then play each other, with the losers being eliminated until there is only one left.
Prepare a pool-style format for your card tournament. Players are randomly placed in pools of four, and then play all of the other players in their individual pool once. Tie-breaking matches can be used in the event of a tie. The winner of each pool advances to single-elimination-round playoffs, competing against the winners of the other pools until there is just one champion left.