Introducing a new pet to the rest of your pets can be tough on everyone involved, especially if you’re bringing home a new kitten or puppy to an adult dog or cat who’s used to ruling the roost. Keep the pets away from each other for at least 24 hours while they adjust to one another’s scents -- this will cut down on aggressive behaviors later. After the first day, feed your pets separately on either side of a closed door. Animals are protective of their food, and getting them to eat in close quarters will let them adjust to this transition.