First impressions are the most long lasting, whether you're a person meeting another person or a dog meeting a cat. Whether you're bringing a new dog or a new cat into your home and introducing them to a dog or cat who's already a member of your family, you want to make that first meeting a comfortable one. Don't leave your pets' introductions to fate. Give each animal time and space to get used to the other.
Keep them separated
It might seem counterintuitive, but when you first bring home a new dog or cat, you want to keep him separate from your other pet, at least physically. Doing so will let your pets get used to the idea of having another animal around, but will prevent them from chasing each other or having physical contact. Introduce your pets while maintaining distance by:
Putting a baby gate in the doorway between two rooms. The cat can be on one side of the gate and the dog on the other. Bring the new pet up to the gate. If the original dog or cat approaches the gate, give him a treat as a reward. Over time, the first pet will associate the new pet with treats and be more willing to approach him.