In most tournaments, you can simply switch to the Players tab and add the player. For match play-style tournaments, the player will be included in the next round of play. If your tournament is using four-player groups and you have a three-player group available, you can click View details for that group, then Change players. There you can add the new player to an existing group. You may also create a new group from scratch by opening the Actions menu for that round and choosing the Add group option.
In knockout tournaments, you also want to assign a number of strikes to the late arriving player to avoid the player gaining an advantage from showing up late. Click the player's name to open the player info panel, then select the Adjust strikes option to add strikes.
When a player leaves early, go to the Players tab and deactivate the player. The player will not be included in the next round in a match play-style tournament. If the player was part of an active match, you can View details for that group, then Change players, and there you can remove the player from an existing match.
If the current round has not ended, click View details for the group and then the Delete results option. After the existing results have been deleted, you can enter a new set of results.
If the round has already been closed, you can adjust the points or strikes for the impacted players. Click the player's name to open the player info panel, then select the Adjust points or Adjust strikes option.
At any point, you can pick a new arena for a match by clicking View details for the match and then choosing the Change arena option.
If you need to manually move players between matches, click View details for the match followed by Change players. That will open up a dialog where you can add, remove or replace players from the match. If you need to switch two players, that requires a two-step process in which you have to Change players for each of the two effected matches in turn.
If a tournament doesn't have enough arenas to cover all games in a round, Match Play will assign as many arenas as possible. The tournament organizer will be unable to assign arenas to the remaining games until one or more of the games have finished, freeing up their arenas. The tournament organizer assigns arenas by clicking View details for a match and then picking the "Select arena" option.