Dogs and cats can learn to get along with one another in the same household. They may never relish each other's company, but they can learn to tolerate each other. It is easier to introduce a puppy to a kitten since they are both babies and have not had bad experiences (yet!) with the other species. But even older dogs and cats can learn to live with each other with a few simple rules.
NEVER ALLOW YOUR PUPPY OR DOG TO APPROACH YOUR CAT. You may think that your dog just wants to be friends, but your cat will only allow so much sniffing before she decides to high tail it out of there, with Fido right on her feline heels and now a precedent has been set. Dogs like to chase small creatures, that is part of their hunting instincts, and besides, he may find it just plain old fun. Keep your dog in a down/stay whenever your cat is in the room. That way Fido is under control while Fluffy is trying to gain some confidence around him. If you do not have verbal control over your dog, meaning that you can stop Fido dead in his tracks with a "NO" or "OFF," then keep him on a leash in the house until you can learn to verbally control him. Just let your dog drag a six foot lead behind him around the house so you can stop him easily. You can also use a squirt bottle set on straight stream (bullet) to douse Fido in the face should he try to chase Fluffy. Praise your dog as soon as he stops chasing your cat. If you cannot get a handle on Fido's behavior, a quality training class can put you back in control of Fido so Fluffy can enjoy her home too. Do not allow your dog to chase ANY small animals. That will only undermine training Fido to leave your cat alone.
ALLOW YOUR CAT TO APPROACH YOUR DOG. By all means, allow Fluffy to walk up and investigate your dog but watch carefully do Fido does not attempt to chase your cat. By allowing this to happen, your cat will gain trust in you and your dog that nothing bad will happen to her. Fluffy will begin to realize that sharing a house with a dog who is not allowed to approach her isn't so bad at all.
ALLOW YOUR CAT TO HIDE IF SHE WANTS TO. Do not force a meeting between your dog and your cat. Allow Fluffy to investigate Fido on her own time. You just need to make sure that Fido is not allow to chase her at ANY time. Give her a quiet room to escape to with her food out of Fido's reach as well. It may take as long as 8 to 10 weeks before your cat will adjust to sharing her house with a canine pal.
KEEP FLUFFY AND FIDO SEPARATED WHEN YOU ARE NOT HOME. Until you feel that Fido is not going to terrorize your cat at any time, DO NOT leave them alone together. Either out your cat in a room with the door closed (make sure she has her liter box, toys and water) or put your dog into a confined place (such as a crate placed in your house).
REWARD ANY POSITIVE INTERACTION BETWEEN THE TWO. Every time Fido lets Fluffy walk by him without chasing her, PRAISE, PRAISE, PRAISE saying in a happy voice, "GOOOODD DOGGG! WHAT A GOOODD DOG YOU ARE!"
GIVE FIDO AN OUTLET FOR HIS CHASE BEHAVIOR. Teach Fido to chase a ball or squeaky toy rather than your cat. Regular exercise can help your dog remain calm around your cat.