Choosing the Right Dog, Carefully Introducing Them.
Choosing The New Dog
If the new dog is an adult, try to select a dog that is to the best of your knowledge, accustomed to other dogs (i.e., one that is socialised).
You should know your current dog well enough to know how well it gets along with other dogs. If it is a naturally submissive dog it probably does not matter too much whether the new dog tends toward submission or dominance.
However, if your current dog is dominant dog, your best bet is to acquire a dog that tends towards the submissive and is smaller than your current dog, Size can be important as your established dog may feel threatened by a newcomer that is a larger breed.
Introduce your established dog and the new addition in a neutral place, like a park or a garden that is new to both animals. It is better they meet outside then neither should feel cornered or enclosed. Both dogs should be on a lead. If your current dog is obedience trained, put him/her in a sit or down stay. Allow them to sniff one another and encourage play, discourage all aggression.
This is especially important if you are bringing home a new puppy as the older dogs will think it has found it and will more readily accept the pup when you bring it finally into your house.
Anxiety or Aggression
Should your new dog show anxiety or aggression, take the introduction slow and easy let the dog realise your existing dog is no threat, do not force the situation allow your established dog to come and sniff the new dog. The new dog should learn to trust the established dog by realising that the he is not going to attack him, and your established dog learns that the new dog is acting either submissive or friendly to him. This fosters trust amongst the two animals.
If the dogs want to play, let them. In fact, encourage them, and do not interfere unless you feel you must. If you are in a secure area, you can let both dogs off the lead at this time.
Bringing Them Home
When you get them home the first thing you must do is establish a spot for each dog that is initially physically separated from each other. In other words kennels, crates, or even different rooms. Never feed the dogs together always feed the dogs if possible simultaneously in those separated areas (if in different rooms, close the doors while the dogs eat). If you must free-feed, the dogs should be placed in their respective areas for the entire time each one's food is down; you can also use these areas for "time-outs" when the dogs are misbehaving.
If the new dog is a Puppy then do not just bring the puppy initially into the house to meet each other, as this may cause problems related to territory and aggression. Because the puppy will probably not be vaccinated then you cannot get your existing dog/s to meet them in a park. Your best bet is to arrange with a friend or a neighbour to use their garden.
Then gently introduce the existing dog to the puppy, if you have concerns over possible aggression then this should be on a lead. Let your older dog find the puppy in the garden, then it will think when you take it home it is because your existing dog has found it.
The second thing that is required is that you must be sure to spend quality time with your established dog. You may even need to increase the frequency of normal activities you would have with your established dog. This should keep him from feeling misplaced by the newcomer.
Finally, be sure and do activities with both dogs. This encourages the dogs to do fun things together, as well as fostering pack cohesion and communication.
Make sure that both dogs realise you control the household and all the resources in and out of the household. See The Alpha Myth
They will need to work out their own hierarchy themselves. Do not get involved in this process, as it may cause insecurity and possibly fights and bad feeling. This is especially true if you support what appears to be the underdog.
In a dogs World, position within dogs is not really based on democracy, it is more a benevolent autocracy. Having said that but they must understand that you are the controller of resources and you are ultimately in charge of all that is good and important.
Stan Rawlinson 2004