Summarize:

Some animals will just never get along. If you already have a dog, think carefully before introducing a cat to your house. No matter how badly you may want a new furry friend, it is unfair to both animals to make such a big change without knowing how it could affect their quality of life. The American Humane Society suggests that a dog that becomes aggressive in the presence of a calm, still cat, or utterly loses her ability to concentrate on anything else, will probably never be able to live peacefully with a cat. This is a difficult, sometimes impossible behavior to train, and if you are relatively inexperienced you may be in over your head. There are many professional dog trainers who can help assess your dog's limits, and work with you to develop a more detailed strategy. This will likely be a slow process. Do not expect too much too soon, and do not be surprised if your animals exhibit animosity or fear. Puppies and kittens that grow up together have the best chance of getting along as adults. If your dog is already fully grown, consider getting a kitten instead of a cat. A kitten is less likely to be afraid of a dog, or to trigger your dog's chase instincts by scampering. If you know someone who has a particularly even-tempered cat, or one that is already used to dogs, ask if you can bring your dog over for a controlled test. This will give you an idea of how difficult it will be to get your dog used to living with a cat. If you are certain you want to bring a cat into your home, start by bringing in things that smell like the catgrooming supplies, beds, etc. Bring things like baby gates, litter boxes, food bowls, and scratching posts into your house before the cat, to give your dog time to get used to these objects.
Be realistic. Don't hesitate to seek help. Keep your expectations reasonable. Start young. Do a test run. Build up to it.