A PlayerController takes input from the user and moves the player.
The simplest controller is a noclip controller. It moves the player relative to the direction they're facing.
The PlayerController class has a number of persistent common properties such as Pos, Rot, Velocity, GroundEntity.
To set the player controller on a player you can set the Controller property. You can do this in Respawn, or the player's constructor.
You can change this property at any point during the game to give the player a different controller. Or set it to null if you don't want the player to move.
The PlayerController shouldn't really ever access the player directly. It can, but it probably shouldn't.
The PlayerController is run on both the local client and the server.
When the Client gets the results from the server, it compares them. If they don't match it snaps the client back to what the server said it should be.
Your controller should always do exactly the same thing.