That dogs and cats could not live together is fortunately not true. Whether this succeeds or not also depends on the character of the cat and the character of the dog.
Own place and stuff for the dog and the cat
Food bowl, make sure that both the cat and the dog have their own food bowl so that they do not eat from each other’s food bowl. Dog food can cause gastrointestinal complaints for your cat. You can also choose to feed the dog and cat at different times, separated fromt each other.
Litter box, make sure you have a closed litter box that is not accessible to your dog. Sometimes dogs tend to dig in the cat litter box.
Make sure there are enough places for your cat and dog where they can have a moment for themselves.
Introduce cat and dog to each other
Take plenty of time to introduce the dog and cat to each other and to get used to each other.
When you already have a cat and a dog comes into the house
If you already have a cat, make sure that when the new dog enters the house you put the cat in a separate room (let your cat get used to staying in another room the week before the dog arrives).
When the dog arrives he can (while the cat stays in the other room) explore his new home at his own pace.
When the dog has found his way around the house, let him get used to the smell of your cat. Rub a cloth along the cheeks (where there are scent glands) of your cat. And put the cloth in the room where the dog is. If your dog comes close to the cloth with the scent of your cat and responds well to this, reward him with a treat. Continue this until your dog is fully used to the scent of your cat. Your cat has already spread its scent throughout the house (by scratching and going with its head and butt with scented glands along furniture, the wall and doorposts).
In the meantime, let your cat get used to the smell of the dog (also with a cloth that has absorbed the smell of the dog). Place it in the cat room where your cat is staying and also reward your cat if it responds well to this.
The first introduction between dog and cat
Make sure that the dog is on a leash and the cat is in a bench or travel basket during the first contact moment. Place the travel basket in a high place (for example on the table). Let the leashed dog rummage on the travel basket.
Repeat this until it goes well.
The next step is to let go of the cat and, for example, take it on your arm or put it back on a high spot such as the table. This gives your cat an overview and therefore a safer feeling. The dog is still on a lead, let the dog (guided by someone else) slowly approach the cat. Keep these contact moments short and reward both animals after they have seen each other. Repeat this until both animals are relaxed, it is important to take the time and not force anything. If this also goes well, you can also let the dog go. Make sure the cat has enough (high) spots where he can go to when he wants to be alone. This will also take some time.
Keep the encounters short during all phases, rather a short meeting a few times a day than a long meeting once a day. The chance that things will go wrong during a long meeting is bigger
If you already have a dog and a cat lives in the house
A cat will need longer time to get used to its new home than a dog. Therefore, the first steps will take a little more time and the start of the introduction will be slightly different than described above. Also, do not let a cat explore the entire house immediately. But set up a room where the cat can stay for the first few days. Is the cat used to his room? Then make sure that he (without the dog in the rooms he is going to explore) can explore the rest of the house at his own pace. The cat will already smell the dog, do not put away a cloth with the dog’s scent the first time your cat goes out to explore. Only when your cat is used to the other rooms of the house do you put the cloth away from your dog. Also reward your cat if it gets close to the cloth. Is your cat used to the smell and does he respond well to this. Then it’s time to introduce your cat to the dog. Do this in the same way as described above.
Sometimes, despite the patience, it cannot click between the dog and the cat. (Just like this can happen with 2 cats). But sometimes dogs and cats become the biggest buddies.
Also interesting: introduce your cat to another cat.