Many cats and dogs learn to live with each other if not like each other. Having a proper introduction between the two critters can go a long way to ensuring household piece. Whether you are introducing two members of the same species or different ones, patience and a slow introduction is important. Start by keeping your animals separate, allow them to smell the other animal’s scent (perhaps bedding or under the door) but avoid physical contact for the first few days. You may want to use a baby gate or X-pen (for the dog) after a few days to allow visual contact while still preventing physical contact.
If possible it can help to work on your dog’s obedience training..commands such as “leave it” , “sit” etc. can be very useful. You may also want to trim the cat’s claws; this allows them to still defend themselves (if necessary) but reduces their ability to cause scratches.
When starting the physical introduction make sure the dog is kept on a leash and the cat is able to “escape” if they want to. You don’t want to force the introductions, let the animals take things slow. Also, it can help to have tasty treats to reward appropriate behavior from the dog and cat. You may also want to start when the dog is naturally in a calm state; this could be after some mental or physical exercise. Keep the sessions short at first and gradually increase the time they spend together (supervised of course). It’s also recommended that using treats to redirect a dog’s behavior (especially if they look a little too interested in the cat) can help to prevent things from escalating. Keep an eye on the cat’s behavior and try to prevent aggression from the cat (e.g. swatting) in a similar manner (toys/treats).
Once things seem to be going well, you can let the dog have more freedom (ie. don’t hold on to the leash) but make sure it stays on them in case quick intervention is needed. Unsupervised interactions shouldn’t occur for quite a while until you are very confident in how they will behave. Occasionally, some cats/dogs will never be able to interact unsupervised but with a good introduction and praise/treats/toys for both animals, the chances of this will decrease significantly.