There are many ways to crown the winner of your tournament. One of the most popular is a single-elimination competition, wherein a team keeps playing as long as it wins, with the overall champion being the group that remains undefeated. Teams are generally seeded, or ranked, depending on a number of variables, including team record and difficulty of schedule, and put into brackets so stronger teams are likely to meet in the finals. Bracketing works on a power of two basis, creating brackets of four, eight, 16, and so on. Although you can have an odd number of teams and schedule byes, the overall calendar will have one fewer game than there are teams (because one team will be declared the winner). If each game takes 90 to 120 minutes, a 16-team tournament will need 22.5 to 30 hours of court time. This could equal three to four days of play.
A double-elimination competition means more organizational work, because each team can lose twice before being eliminated. This means teams get more bang for their buck by being able to play at least two games. Because it's bracketed, there will still be an overall winner. For scheduling, an eight-team double-elimination tourney will need 15 games.
In a round-robin tournament, teams are divided into pools, and they play everyone in their pool either once or twice. The team with the best record wins. In some tournaments, after a round of pools, a single-elimination competition takes place so there's an overall winner. The disadvantage to this format is the amount of rounds needed. While a 16-team single-elimination tournament takes only four rounds, a 16-team round-robin tournament requires 15 rounds of action.
A 3-on-3 tournament is exactly what it sounds like: Teams of three players compete against each other in a pick-up game type of event. These tournaments are often organized for charity events, and the event director sets the rules. Most often, these include playing on a half-court, winning by a certain number of points or within a time frame that's shorter than a standard basketball game. A 3-on-3 tournament can be a large competition involving dozens of teams across all age ranges. Teams are grouped into divisions, usually based on age and/or gender, and they often play in smaller pools, with the winners going on to an elimination bracket within the division.