I am about to bring home a puppy, and I currently have an adult cat living in my home. What is the best way to introduce the two? I imagine my cat will be a little mad at first, but I also don't want any swatting or clawing to happen.
I have been in this situation before, and to be honest, at first I didn't think it was going to work out! I gave up one day and decided to just let them work it out (supervised, obviously) ! IT WORKED! They were best friends.. But make sure you give the same amount of attention to the both of them, making one feel lesser could be bad. Also lots of treats for your cat isn't a bad idea!
I'm currently in a similar situation- I have three dogs and a cat and just brought home a new kitten. My dogs have taken well to him but my adult cat doesn't seem very happy about it. I make sure to give my adult cat a lot of treats, love and attention- especially when the kittens around so that he doesn't harbor any more resentment. I also make sure they're not together unsupervised and that my adult cat still has his own 'safe space' to go to whenever he wants to get away. They seem to be doing increasingly better.
It may be slightly different with a puppy, but I would say that its very important to make sure your cat has access to an area that the puppy doesn't- like a high shelf, or a room that only your cat can get to so that in case the puppy is playing too hard or bothering him/her, he/she can escape. That will at least lessen the likelihood of swatting or clawing and help your cat feel less threatened.
In simple words, let them be ! I've had dogs most of my life and my mother used to have 2 cats when I was younger. There is really not much you can do about it, I think they just learn to get along with each other in time. Since you are just having a puppy, you should not have to worry about much...