Keep them separated from one another initially, using crates. There’s no point in setting the new dog up for failure. If he’s quiet and good in his crate, reward him with treats for his good behavior, and simply ignore him if he’s putting up a fuss. Use a baby gate to help keep the dogs separated through the initial introductory phase.
Walk them separately in the beginning.
When one is crated and the other is free, reward them both with treats for good behavior and a calm response to the other dog. Rewards work better and have a much longer impact on a dog than reprimands.
Feed one dog in his crate and the other in another room or another crate, so neither feels threatened by the other when there’s food involved. The same advise applies to high value toys and treats. Keep them separated and do not allow a rivalry to develop.
If there doesn’t seem to be a huge problem between them, you can begin to walk them together, on opposite sides of the street. After that has gone well for several days, then you can allow them to meet on neutral ground, such as a nearby park. If that goes well, then they can walk home side by side, and have their walks together after that. It will still be too early to allow them to be together in the house – give them a few days of enjoying their walks together.
Once that is going well and they’re looking forward to seeing one another, then you can carefully let them meet in the house, preferably when there are two adults present. USE A LOT OF TREATS to reward them when they’re good, just be very careful not to inadvertently introduce food aggression at this point. Give each of them the SAME treat at the SAME time and do not allow either of them to try to steal the other’s treat. Collars and leads would be quite useful at this point, just so you have a way to maintain control of the situation if it appears to be getting out of hand. Remember, outdoors is one thing – in the house is a totally different environment for a dog, and one or both of them might be protective about having an “invader”. That’s why it’s important for them to get to know one another on neutral ground and to see one another in the house (but safely apart from each other) for a while. It will be much easier on both of them (and you and your family) if you take the time in the beginning to introduce them carefully.
This can be quite a lengthy process – up to two months – so don’t rush the dogs into a situation that they might not be ready to handle.