Coffee break just means that the dweller is not assigned to a room or out exploring - they just wander around the vault, not contributing anything or leveling up, but still consuming your resources.
Dwellers go on coffee break automatically when they return from exploring the wasteland, or when they grow up. Just drag them to the room you want them to work in and coffee break is over. They'll keep working in that room until you put them somewhere else, or until they get swapped out with another dweller you drag into a full room they're in (they'll switch rooms with that dweller and start working in the new room right away).