Normal victory conditions are last man standing or most kills. Unless stated otherwise, all tournaments are single wave to keep them quick. Usually only the last tournament of a series is with multiple waves.
Then the tournament coordinator will pick people and ask them to start rooms (usually T1, T2, T3..) depending on the number of people present. Then everyone else will join one of these rooms. Inside the rooms, they will decide who will host and when everyone is ready, the tournament coordinator will give each rooms the signal to drop.
After the battle is completed, the people will return to kali. Those who are going on need to join a room called t?-round2, i.e. for the second tournament: t2-round2 . Everyone else should join a room with the number of the next tournament. So if we just fought in tourney #4 and lost, we go to a room called tourney5. If we just fought in tourney #4 and won, we go to a room called t4-round2. People will wait in these kali rooms until all groups complete their battle for that round.
In the interest of speed, the second round of a tournament is fought at the same time as the first round of the next tournament. This ensures that no one is left waiting for an entire round of combat.