A common misconception about dogs is that they attack all cats on sight, or are incapable of living safely and peacefully with cats. In fact, dogs and cats can make wonderful friends and forge powerful, long relationships, but only if they are properly socialized to one another and have no pre-existing issues. Introducing a dog to your cat is a delicate process that can take several weeks.
The primary issue with cats and dogs is not a default hatred, but an incompatibility of instincts. Cats are programmed to run in the face of danger, and dogs are programmed to chase things that run. This can have disastrous consequences if it plays out in your living room. Dogs and cats are social animals and can live in peace, but it is not something that is guaranteed to happen within the first few minutes of their meeting.
Knowing the Dog
Some dogs are not good with cats. If you rescue a dog and the shelter is clear about his behavior around cats, it may be best to keep the two separated and work with a professional trainer to establish a safe relationship. If the dog has no pre-existing issues with cats, socializing him to the cat (and vice-versa) shouldn't prove to be too complicated. Before you start socializing, make certain you understand how your dog will react to a cat.
Making the Introduction
Ensure the cat has an escape route. If the cat feels trapped, he will react with claws and teeth. Make sure the cat has a safe place to hang out without the dog, such as a separate room for his litter box and toys. Allow the cat and dog to check out each other's spaces without actually meeting so they can get used to one another's scent. Next, introduce them through a fence or baby gate. This lets them meet in relative safety. When you finally introduce them in the open, use a dog leash to keep your pup under control. Have your dog work through obedience commands around the cat to establish a pattern of good behavior.
The most important thing about letting your cat and dog interact is that you stick around to enforce rules and supervise. Chasing the cat should not be tolerated, and should result in a play timeout for your pup. Do not leave the two animals unsupervised until you are certain they can get along in safety. Socializing a dog and cat is possible, but it takes time. Do not be afraid to move slowly through the steps to ensure the animals have the safest and most rewarding relationship possible.