When a Pokémon is sent out, its external move is shown at the top-right corner of the screen. With default controls, an external move can be used by pressing 'g'. If a Pokémon is able to use multiple external moves, the player can cycle through them by pressing (by default) 'b'.
After using an external move, a cooldown timer will be imposed on it, graying out the move's icon, and it cannot be used again until the timer expires. The duration of this cooldown depends on the type of external move and may also depend on the Pokémon's stats. The cooldown is independent per Pokémon and continues to count down even if the Pokémon is withdrawn.