This is what I use and it is very successful. It involves a bit of expense though and some patience, but it works for every stray kitten or litter that comes through.
I have a huge steel cage in our front room. Normally, the door of this cage is always open and this is where our dog sleeps, or where she goes on command when someone comes to the front door. It is large enough for 2 german shepherds to turn around and lie in it. (that is the expense I was talking about). I call it our Hospitality Cage, and when we get new kittens, I put them inside the cage, with all their necessities of course, and close the door. This gives the dog and the other cats a chance to get to know the newcomers, and keeps the kittens safe.
You watch for the dogs reaction, how hyper they get, how aggressive, if you see aggression then you need to use this process only about 20 minutes every day for about a week, other than that keep the kittens safely tucked into another room, or the dogs outside. Put the dog's blanket inside the cage, then once the kitties have had it a few days, give it back to the dogs. Watching your dogs is key- watch the body language. The kittens will hiss and spit that is normal, but the more you introduce them together (safely) the easier the transistion is. Once the body language is relaxed, simply leave the cage door open and let them meet each other on their terms, supervised of course.