Introducing doggie and kitty to each other can be stressful. We know most cats will not appreciate what a dog has to bring to the game and cats have some mighty impressive weapons that can cause damage to dogs and people, so we need to proceed with caution.
The following instructions are only intended for dogs that do not have a history of doing damage to cats. They may be dogs completely lacking in experience, dogs that have chased, curiously sniffed or gently played with cats, but they display no predatory behavior to them. Even under these circumstances the introduction can be stressful.
Because these introductions can be stressful, you want to take it slowly. The process should not be a single event, but an event that occurs each day over a period of time. You want to think about it as a training opportunity for both the doggie and the kitty with a safety net in place.
You will need to protect both animals from possible injuries during the introductory period. For safety the dog will be on leash with a capable person handling it and the kitty will have its front claws trimmed.
Now that you have taken steps to protect the animals from harm you can set up the training environment. You need two people (one handling each animal), extra delicious treats for each animal, and a space that allows the animals to be in sight of each other but is large enough for the animals to relax. The kitty will be brought into the room first, and be on the end of the room that the dog will not be entering or exiting from. If the cat will relax quicker by being on a perch, make sure that is in place before you begin training.
Once the room has been set up, take the kitty into the room. Settle it in its spot and start giving it a deep relaxing massage. You want to get the cat relaxed. Once the cat is relaxed bring the dog in on leash, entering from the far side of the room and staying on that side. Each time either the dog or cat looks at the other animal, quietly cheer and give it a tasty treat. When they are not looking at the other animal, then give them a deep relaxing massage. If either animal cannot relax in the presence of the other you will need to increase the distance between the animals and may need to seek professional help. Your first training session should last no longer than 5 minutes. When the 5 minutes are up, remove the dog from the room and let the cat check out where the dog used to be. After the cat leaves the room, let the dog in to check out where the cat has been. You can have multiple training sessions in a day as long as there is a three-hour break between sessions.
Regardless of how long your training sessions are you will want 2 training sessions in a row in which both animals are completely relaxed before you make the training more advanced. Once you have two sessions in which both animals are relaxed you can have the animals a little closer. You will systematically over time decrease the distance between the animals, keeping in mind you need both animals to be relaxed. When it comes time for contact, sniffing is appropriate, but pawing, scratching, barking, hissing and biting means you took the process too fast.