​Introducing a puppy to resident cats may be an easier transition. A smaller puppy may not seem as threatening as an adult dog however an energetic puppy could prove to be more of an annoyance to cats than a calmer adult dog.
Research the dog's breed: Certain breeds may be less safe around cats such as dogs with a high prey drive like terriers and sight hounds. Herding breeds may tend to chase and nip cats in an attempt to herd them. Hounds and retrievers are thought to be better with cats as they may be gentler and more likely to consider cats as members of their "pack." Individual dog behavior will vary with each dog so generalizations can't always be trusted.
The dog should be kept under control . The dogs must remain confined and or on-leash at all times during the initial introduction and until the dog can prove to remain calm around the cats.
A crate should be used to confine the new dog allowing the cats a way to sniff and investigate the dog without the threat of being chased. Remove the cat from the dog crate area if the dog becomes agitated or excessively vocal.
Be prepared for your cat to hiss and be otherwise unwelcoming to the new dog. Cats take time to adjust to newcomers and may only approach the dog with cautious curiosity while the dog is confined and/or sleeping.
Allow the cats to have access to a room or area that the dog cannot enter. Place a pet gate in the doorway to a room and leave just enough space underneath for the cat to fit under, but not the dog. This will not work for smaller dogs or puppies in which case you can consider cutting a cat-sized hole in the mesh of the gate higher up.
Ultimately, the cat needs to have a dog-proof escape route in every room where he or she will come in contact with the dog. Even if the escape is to a Table or the top of a bookshelf.
Keep the cat's litter box, food and water in an area that is not accessible to the dog. Dogs cannot resist eating cat feces and/or cat food so these tempting treats need to be kept where the dog cannot get to them. You can block off access to a room by using a pet gate or installing a small pet door that only the cat can fit through. Cat food and water dishes can be moved to a counter-top surface if possible. Also, keep cat toys picked up and confined to the dog — free space to prevent a possible choking hazard for the dog.
Teach the new dog commands that will exercise self-control from day-one. Using the leash and treats, your dog should become accustomed to commands such as "leave it," "sit," and "stay."
Supervise all interactions between the dog and cats until you are confident the dog can remain calm around the cats. Short practice sessions with no leash should precede any attempt to leave the dog loose without supervision.