Cats and dogs may seem like mortal enemies, but there are many examples that support the idea that they can coexist quite peacefully. Cats and dogs do not hate each other simply because they are cat and dog, and it more often than not comes down to how they were introduced and that crucial period where they had to get to know each other.
Both cats and dogs are similar in terms of their territorial instinct and we need to understand how they work. Wild cats, from which the common house cat was slowly bred, are generally quite solitary. They do not usually live in large family units unless they are raising a litter of kits. Their territory is important to them and they will defend it as well as mark the boundaries with urine. Since cats have exceptionally high territory instinct especially at home, any additional members to the family will need to be examined in detail. Changes in a cat's life including new additions to its territory can be very stressful, especially for a cat who leads a very static life.
Dog ancestors, unlike cats, prefer to live in big family units, and marked territory where they hunt and live. While a dog might perceive all the members of its owner's family as its pack, it will still be as curious as a cat and possibly defensive around new additions such as a cat. With a bit of time however, a dog will come to understand a cat as just another member of the pack, albeit one that might ignore him completely.
Because a cat and a dog will approach a new addition to the family in a different way, a pet owner must consider this when allowing them to meet each other. A dog will want to hop right in and test the cat, sniff it, see if it wants to play or if it will try to be dominant over him. A cat on the other hand needs time to observe from a distance. Cats are naturally more cautious and are unlikely to dash towards unknown objects.
You should keep the dog outside the house first before you locate your cat. Once you have discovered the cat's location, bring the dog in on a short leash. Enter the room with the cat and have your dog sit and stay or lie down. Your objective is to give the cat enough time to understand the dog a little bit and to get used to his presence. You will want to keep your dog as calm as possible, so before the introduction, consider taking the dog on a long walk. Once the dog is sitting, reward the dog and the cat.
The first introduction doesn't need to last very long, but you will want to keep the dog on the leash until the cat has a good idea of how the dog is when acting calm. Once the cat begins to act a little more relaxed, you will know that it is time to take the dog off the leash.