It is generally recommend that the cat is confined to a room or two by a closed door, and the two of them first get used to the scent of the other animal but don't see each other. When they are settled with that, let them see each other through a barrier like a baby gate. If the dog tries to go for the cat, stop and redirect the dog to a toy. Cats are NOT toys. Never force the two together.
Start slowly. Smell but no sight, sight and smell but no contact, then dog on lead and cat loose (so you can control the dog and redirect undesired behaviours and show what is desired) and eventually cat goes in dog-free zone if not already there and the cat is allowed to come out to the dog on the CAT's own time.
The trick is making the cat feel safe and as if they have a safe area. Next is training the dog not to chase and torment the cat. This may mean on leash in the house at times so you can stop the chasing of the cat, and redirect to better toys. In addition, a good obedience program (even a refresher if the dog has gone through one already) is a good idea.
First, set up a Dog-free zone. If the cat can fit through a hole the dog cannot, you are all set here! Get a baby gate and fit it in a doorway.
Cut a door in it (file down sharp edges and cover the cuts with duct tape) and this will keep the dog out of the cat's safe zone. In this zone, you will put food, water and the cat's box. Another option is to install a cat door in a room such as your laundry. If the dog is small enough to get through a cat door, then you may have to teach the cat to jump a lower baby gate to escape the dog. A Dog-free zone gives the cat a place to get away and a feeling of security.
If a cat teases a dog or bats at feet as the dog walks by, you can allow the dog to chase the cat a little. Learning is a two-way street. Just as the dog needs to learn not to torment the cat, the cat needs to learn not to torment the dog.
In the best cases, the dogs and cats will play together and maybe even sleep together. Even though this is very common in some households, it is recommended that cats have their dog-free zone (also keeps the dogs out of the litter box and from stealing cat food at meal times)!
Pulling out hair...at wits end!