Oh, what you meant was how to introduce a new dog to a cat. Ok, it is the same thing, since there are only two of them.
It is not uncommon that dog and cat don't get alone. Some of them can be territorial toward other animals in the same house, and some of them can be jealous of you now pay attention to others instead of them.
In my opinion, you should make them get comfortable with each other by creating situations where they have to be together in the same room, in your presence of course. I am thinking maybe you can schedule group meal for the two of them at the same time. While they should eat out of different bowls, you may place their food in the same room at the same time, then call them over at the same time. Or maybe have the dog in the room first, then call the cat. So they won't have any confrontation on the way. If the cat is remotely wanting the food, she will have to come into the same room to eat. You must not do anything with the dog to make the cat jealous, but you also must stay close to prevent any physical confrontation.
Ok, it is the same thing, since there are only two of them. 
