Essentially, they didn't. Rats were considered decent eating on long voyages, fried in some flour or a bit of pounded hardtack -- especially by the hungry young gentlemen in the midshipmen's berth. What they could do is to attempt to mitigate the damage rats would do to foodstuffs, by keeping cats on board, killing rats on sight, and keeping flour in a tin-lined breadroom (the theory being that rats won't gnaw through the tin). But rats and other vermin were unfortunately persistent parts of life on board a sailing ship.