In the beginning, the new pet and the established pet should have limited contact and interaction. If you are introducing a new dog to an established dog, an x-pen in the room where you spend the most time will help. The new dog should be in the x-pen with water and a bed to sleep on, limiting free access to the entire house. This will help the established dog maintain the same routine and relationship with the owners, and help him/her realize that, other than the presence of the new dog, nothing has changed. An x-pen in the bedroom can also be helpful, allowing the established dog to sleep undisturbed.
The established dog's toys should be given one at a time and the new dog should have their own toys, too. Later, as the relationship between the dogs becomes accepting of each other, they may choose to share toys.
Feeding separately is also advised.
The established dog should be taken into the yard or for a walk while the new dog is harnessed and leashed and walked through the house daily. This helps the new dog become familiar with the home without the pressure of the other dog's presence. Dropping treats in each room helps convey that each room is part of the home and discourages the dog from thinking about pottying in other areas of the house.
Walking the dogs together side by side, with two people, in areas that are interesting for the dogs to sniff and do their "doggy" things helps build their relationship.
Taking time and not forcing the dogs to spend too much time together increases the chances they will be compatible.
If you find you are having difficulty helping the dogs establish a relationship, seek professional help from a qualified behavior consultant that uses force-free behavior modification methods.