It worked by having one player use a GameBoy Advance (connected to the GameCube with an adapter) to (privately) operate Pac-Man while the other three players use GameCube controllers to operate ghosts from the TV.
Additionally, to give Pac-Man a better shot at winning, the three ghosts play from a third-person 3D perspective, rather than top-down.
The ghost that caught Pac-Man would get to take over as Pac-Man (which would inevitably result in a tangled mess of cords by the end).
It was a great couch 3v1 game.
The WiiU had similar mini-games in Nintendo Land [2], with one player operating the Wii U gamepad, while the others played from the TV.
I miss the era of couch multiplayer games.