An older or very calm cat will be more likely to mesh with a more relaxed dog. If you are adopting a kitten, they might be more interested in hanging out with a more playful dog. Remember that you have your own preferences about who you live with. Make sure you respect that your pets might have the same preferences.
Tire your pup out at the park, make sure everyone has eaten and relieved themselves. If your pets are comfortable and happy, they will be more amenable to an introduction.
If you are bringing in a new dog to a cat's house, it is important to make sure the cat is comfortable and happy. Maybe let the dog spend some time in a different room of the house to get used to the smell of the cat and vice-versa. Let them get familiar before they even see each other, and reinforce positive feelings toward the smell with treats.
This is a good idea if your dog is particularly playful or rambunctious. You cat may get spooked and react negatively if the dog is too overwhelming. Signals can easily get crossed in these situations and your dog's "let's play" can quickly turn into "I'm going to eat you!"
But proceed with caution! Once everyone knows there are no immediate threats, you can start leaving them alone together. Keep your eye on their interactions when you are around and be on the lookout for any tension between them.