I just bring puppies into the yard or house and plop them down.
I usually do the same with any other dog I bring home... I know that neither of my two dogs are territorial, so as long as the other dogs aren't dog-aggressive, they meet in the back yard off leash (unless I'm testing a dog whose dog-status was unknown) so that there's a little more space.
I do 2-5 dog introductions at work on a daily basis, so I'm really desensitized to these at this point.
I just bring in a puppy and plop it down. I do not subscribe to moving everyone to "neutral territory". Our territory is not neutral, it's mine I decide to gets to be in it and where and when and for how long. My dogs are cool with this arrangement. They love getting a new toy, I mean puppy.
I think it depends on how young the puppy is and knowing the dogs you have now. I'd keep an eye out and give them some time to adjust. My old dog has also gotten along with cats, dogs and people, completely reliable and trustable. But I brought a half-grown pup/dog in and she is showing some stress/anxiety around my old dog, who wouldn't hurt a flea. So slow we go.
My two already met our new puppy who's coming home Friday. We had to take our two to her foster family's house and we just went ahead and brought them inside. Our new girl was running free in the house and barely cared that two big dogs were coming into the house. They all were fine.
Friday though, we may keep everyone outside and let them get a feel for one another. We did that when our 2 year old came home. The 14 year old is very moody so we did their initial meeting on neutral grounds. I don't think I have to worry so much this time around with the puppy though.
Thanks for all of the great posts here. I will be introducing a new pup this upcoming spring to my resident 4 year old female GSD and 2 older felines that are very dog savvy. There's so many different ways to do this but I have a fantastic trainer that has taught me so much about the breed. I'll definitely be following this post and will update my experience when the little guy joins us!