New teams are chosen each turn. The teams are chosen by the player designated "first player" on the voting board.
You keep score as individuals so you can mix and match team members with no problem. It's really clever that as the game progresses you stop trying to pick the best player on your team and start using the individual scores to help you pick who to put on your team.
It's a great mechanic and really amps up the tactical strategy for that turn.