The ideal way is to have both a puppy and kitten grew together naturally. Dogs and cats can become great friends, but just like with people there are some who might not get along even with what you try to do.
It can take a while for your cat and dog to become comfortable around each other; there are no quick fixes; it could take weeks or even months. One of the most important things not to do is to try to force your cat and your dog to meet each other – they have to do it on their own terms. Both the cat and the dog need their own place, somewhere safe and where they can go. A dog cage is ideal for your dog and the cats also need a bolt hole, such as a hidden room or the like.
When first introducing your dog to your cat, ensure the cat is secure in another room and your dog on a leash. You must have control of the situation and you must be confident in what you are doing because there is really no room for human error.
If your dog is not good at listening or focusing on you, then work must be done, obedience training and enrichment games such as Canine Parkour will help with this. You need to have your dog’s full attention.
If it starts barking tell it to leave it if that doesn’t work, try some water and vinegar in a squirt bottle. Squirt it into your dog’s face. A dog crate is also a useful tool: crate your dog and let the cat roam freely in the room. You have to be watching 365 days a year in other words there must be no distractions. If your dog starts barking you can also cover the crates so that the dog can’t see until it calms down. Depending on your situation, introductions may need to be small and often. It is always a good idea to never leave the cat and dog alone if you are out all day. Then be sure they are both safe and apart from each other.
After a few weeks of constant and consistent training, you may be able to let your dog off the leash or get out of the cage with a brim and watch how the cat and the dog interact. Some might think this is unfair or harsh on the dog but its better than the death of your cat. Even after all this training, your dog and cat might be okay when you are around, but when you are not around, all the odds are off.