Introducing a new dog to your current pets can be tricky. Dogs especially are very territorial, both of the home and the family. Dogs feel the need to protect both, making it difficult to integrate new pets.
Do not bring any of your current pets with you when you pick up your new pet. Also, try to wear clothing that smells like your pets (hold them and pet them before you leave to get the new dog). This will accomplish two things: One, you get bonding time with your new pet without the scrutiny of your other pets, and Two, the new dog will smell the other pets on your clothes and have an idea of what he is in store for. If possible, have another person drive you to pick up the new pet so you can sit in the passenger seat and bond on the way home.
Let the new dog check out the surroundings when you get home, before you go inside. That will give him time to acclimate.
Leave the new dog out front (supervised, of course), go inside and pet your current pets again, so they get the new puppy's scent. Then lock your pets up somewhere out of sight, either in a bedroom or outside (in a place where they will not be scared or upset--usually somewhere they spend a lot of time). Go back out front and bring the new dog inside and set him on the floor so he can explore.
After 20-30 minutes, the new dog has explored quite a bit and your other pets are getting antsy (and you probably are too, just wondering what they've done to your bedroom!). Put the new dog in a crate and leave the crate in the middle of a room in plain view. Use a crate large enough that the new dog has personal space, but it should be an open-air crate with wires, so the other pets can see and smell the new puppy.
Let your other pets out of the room. Do not coax them to see the new dog. Pretend you have no idea the new dog is even there. Your pets will "discover" the new dog, and probably become excited (like kids at Christmas). At this point, you should act surprised and happy about them finding the new dog, maybe even give them treats (if they are acting in a non-aggressive way). Let everyone interact, leaving the new dog in the crate, for at least an hour. Give your pets treats and praise when they show behavior that you are satisfied with. Do not yell at your pets if they become aggressive, and do not get angry. Your pets know when you're angry, and this is a happy occasion. If you act angry, your pets will assume it is because of the new dog, and they may feel they need to protect you from it.
If after an hour, you are satisfied with everyone's behavior, let the new dog out. Always remain calm, no matter what happens. This is a stressful time for your fur-babies, and you need to be the glue that holds it all together. Let the pets interact. Do not get involved unless you fear for the safety of one of the animals, but always stay close by. The dogs will probably sniff each other and circle each other for a while, and may decide to ignore one another, or try to play. Either of these scenarios is fine. If they don't want to interact, DO NOT force them to. If one of the dogs becomes aggressive, immediately separate them.
Do not favor the new dog. You do need to bond with your new dog, but you don't have to do it in front of your other pets, leaving them feeling neglected. You need to give each animal the exact same amount of attention over the next few weeks, so nobody develops a jealous attitude. If your other dog is mad at you, don't try to force him to interact with you. He will see that the new dog is getting attention, and he will eventually come around, though it may take time and get frustrating.
Also prepare a place in your house with some chew toys and a bed. Make sure it's closed off from the rest of the house and other pets if you have any. This area could be a crate or a room. That way if you leave the house the new dog won't destroy the house. If it's in a room make sure it's tile.
Be patient! That is the most important thing. You may want to force the animals to get along, but that does not work. They will come around eventually.
Never show favoritism to any of the pets. Animals are very in-tune to human emotions, and they can sense when they are not your top choice. You don't want any hurt feelings.
Have a positive attitude, and your pets will follow.
Do not ever leave the new dog alone with the other pets unsupervised.
Don't take the new dog back after only a few days, just because your animals aren't getting along. You are then sending the message to your pets that they control your house and that they get to say who stays and who goes. You will be creating a monster, and you will never be able to bring home another new dog without getting the same results.