When they switch with a player, they become that player's role, and the other player becomes the Thief. Role specific disguises are also switched.
Selecting a player to switch with is an immediate effect, but switching roles is an end night action and happens after any other end night actions such as night kills. The Thief can switch with a dead player, if the player was alive when they selected them.
When switching with another player, all their channels are switched. Effects such as being powdered are not swapped. Effects are kept after switching, even if a player's new role cannot have that effect. In those cases the effect becomes dormant and does nothing; it will become active again if the player once again switches role.
If the Thief does not select a target, a random player is chosen. Each Thief may only select players that have never been that thief before.