First, you will want to introduce the dogs prior to moving day so that neither feels threatened on the big day. It's a good idea to do this in a pleasant environment on neutral ground, not in what will be their shared home. Both dogs should be kept leashed during the meeting, with a caregiver for each dog. This ensures that it will be easy to separate them if they start to show signs of aggression. If there is growling, or other signs of aggression, separate the dogs, distract them each with play, and then try again.
Don't scold them. It's important that you do everything possible to make the experience pleasant, as this is what they will remember about the other dog. The transition will be easier if they associate each other with treats and a fun day at the park, rather than being reminded of a scolding when they see the other dog. Of course, part of ensuring that the experience is pleasant is to be sure that the dogs are up-to-date on their vaccinations.
An older dog and a puppy
If you have an older dog, and have brought a puppy into your home, the older dog may feel that his turf is being invaded and be wary of the puppy. To help the older dog feel more comfortable it's a good idea to wait until the puppy is asleep before you reintroduce the dogs. While keeping a firm grip on the older dog's collar, let him sniff around the puppy. Also, make sure the older dog gets some quiet time alone with you during the first few weeks of him sharing his home with the puppy.
If you have two puppies, it is important that you spend equal time with both. Just like young children, they may fight over food and toys if you don't take steps to prevent this behavior. The puppies should always be supervised and leashed when they are brought together and separated when they are left alone. This will ensure they don't have the opportunity to fight over puppy toys or get too rough with each other. As well, ensuring they have their own eating areas will prevent fights from breaking out over food.
Using the preventive measures given above will go a long way in providing your dogs with a pleasant atmosphere, and lifelong canine companion.