There are a couple of fundamentals to follow when adding a new dog to your pack that will make all the difference in how smooth the meeting goes. I am going to assume there is only one other dog in the house for this and will give more details later. It is always best to look at a few basics like sex, energy level and age to understand how your current dog is seeing things.
-If you have a male you should look at adding a female and vice versa. The reason choosing opposite sex is important is because there is a more natural order and problems are less likely. Female on female can be some of the most intense behavior there is. Chick fights can be crazy!!
-The new dog should be a lower energy level than your current dog. The energy level is important because it shows respect to your current dog. If your dog is six years old and kind of mellow and you get a ten month old boxer it's not a good match. It's like bringing a ten year old to a retirement community.
-The new dog should be slightly older than your current dog. If your dog is 2-5 years old you should get a dog that is about 3-6 years. This helps keep the energy level equal and it increases the chance of the dogs getting along. Don't get a dog with the idea it will help your puppy figure things out. This is only the case if the older dog is balanced.
-Getting a second dog to keep a current dog company is not a good reason. That usually tells me the current dog is acting up and you think a new dog will occupy him when you are not home. If you do not have control of your current dog and you get a second dog you will most likely end up with two dogs you can't control.
Once you have selected a dog the best introductions take place on walks. When I help a client do an introduction I first walk the new dog with the owners and teach them the proper fundamentals of the walk so the dog sees them as a leader from the start. Once they show me they have proper control we will add their current dog to the walk without letting the dogs smell or meet yet. I want to walk for a few minutes and get the dogs calm and following me.
Once they are in a submissive state of mind (ears back and calm) I let them go through the brief ritual of greeting. I am looking for mutual body language and dogs who are equally interested in meeting one another. I let them do this for 15 seconds and then I keep walking. If either of them gets excited I stop the meeting and start walking. I will repeat it again and again until they are comfortable with one another.
This ritual is important because it helps the new dog see you as a leader from the moment he meets you and tells your current dog you have control of the new dog. You can essentially tell him anything you want from that point forward if you take your time and follow this process.