This weekend probably we are headed to the pound to pick out a new kitten, or possibly two. We already have a friendly mixed breed dog. We know the dog tolerates cats because the neighbors have had her over at their house for a week while we were on vacation, and they have 4 cats and she didn’t bother them.
But it’s different introducing new cats to her own territory. Any suggestions on how to do this so it is the least traumatic for both the dog and the kitty?
keep them physically out of sight from one another. let the cat get used to one or two rooms full of dog stink. remove cat from the room daily for a bit, still keeping them out of sight, and let the dog in to sniff around and also stink up the room (have the dog roll and lay on things in the room). over days move the separation closer and then within sight of each other.
IME, cats–even kittens–hold their own quite well when introduced to a dog. It’s generally the dog that is afraid of the tiny interloper.
Puffy/condescending cat, and curious/friendly/slightly alarmed dog…
I always found it amusing.
However, Johnpost’s advice is obviously the wiser move.
I just get a kick out of outraged kittens. So tiny and so angry that they can convince an 80 lb dog that they are king. 
In my expirience:
Introducing cats to existing dogs; no problem.
Introducing dog to existing cats: problem.
I had one dog that just sulked around the house for a day or two because we brought a cat home. But he soon got over it; cat and dog even played and slept together.
Make sure the cat’s nails are trimmed in case the first encounter goes bad.
Try to find a kitten that seems confident and bold, rather than timid and skittish. I’ve found that the personality self-reinforces.
A skittish kitten who bolts at the sight of the dog immediately sets off the canine chase instinct. Kitten now learns it has reason to fear the dog, and runs when it sees the dog, who automatically runs after something that runs away. Vicious cycle ensues.
A confident kitten will look at the dog with a “What’s up, dude?” expression. No chase instinct is set off. Kitten learns it has nothing to fear from the dog, and they wind up being photographed sleeping together. Much "awwwwww"ing ensues.
When we brought home a kitten to a household that already had an adult cat (not a dog, but close enough for the OP’s purposes) we brought Kitten inside, in a carrier, in the middle of the afternoon while Cat was passed out asleep.
By the time Cat woke back up, had his dinner, etc. the new Kitten had been in the house for several hours. By the time Cat got around to noticing that one bathroom door was permanently closed and had some interesting smells coming out the cracks, Kitten had been in the house for a day or two.
Gradual transitions and introductions work best. Let the kitten get used to you for a day or two, first, before starting on introducing the doggy.
Remember its not her territory, to her, you are the Alpha, its your territory and if she is a friendly non-Alpha, if her alpha says “this is part of the pack” it is.
We just did this with our friendly mutt and a new kitten. We let the kitten out of the carrier with a hand on the dog. The dog sniffed, the kitten ran behind the couch, the dog showed “friendly interest” - within three days he was letting his tail be her cat toy.
Our dog is trained not to come upstairs, so for the first week (and still) the upstairs (and the basement) are kitty territory. She figured out darn fast that she could sit six stairs up and look at him, and he’d just sit at the bottom of the stairs and look at her.
Dogs love bacon. If you coat the kitty in bacon grease he will love the kitty too.
I agree with this. I can’t think of a time where the dog didn’t come around to a cat. When I was kid, we brought the cat home, the dog barked at it once, the kitten ran behind the couch and the dog was like “OK I can’t get at it so, that’s that.”
After that they spent the next ten years, each pretending the other didn’t exist. But there was no issue.
To play it safe, make sure the kitten knows it has hiding places the dog can’t get to. Like behind the couch or refridgerator.