Moving and Seating Players
For one or two tables, the fairest way to seat people is to have people draw cards. Then the player who chose the highest ranking card gets to pick their seat and they get the button. See our page on rank of suits if more than one player draws a card of the same rank. If there is more than one table, use one color or suit per table. Typically players getting moved to a new table are put in those empty seats. Generally a player sits out a few hands until he/she gets the button if they are in early position. This is done to avoid having a moved player getting hit by blinds too much between tables. If you need to take a player off a table, take the player who is about to be big blind. This is done because moving to a new table is a serious disadvantage because you haven't had time to get to know how the other players are playing. The moved player also loses any table image he/she may have been building.
If there are more than 40 players, you'll need to make some custom cards that say the table and seat number. Put those in a bucket, then when people pay their buyin, have them draw a custom card. Now instruct your dealers (or all players) to hand you (the tournament director) each person's custom card when they are eliminated. This way when you need to move a player you have the cards in front of you and you'll know which tables are lowest in players. Once you notice that a table is low enough on players to be broken up and split among the remaining tables, do it. If the game is just a friendly game, you can play the game yourself, but with larger tournaments, as the tournament director, you should not play the tournament yourself. Not only does this ensure fairness when making decisions, but almost assuredly, you will have many things to take care of throughout the tournament.