Walks.
Take them on walks together. It seems overly simple but this is one of the most effective ways to introduce dogs successfully. I like to have each dog on a 6 foot leash and start away from any dogs home. It could be a block away, or at a park down the road, just not directly in front of the house.
This walk is what I consider a structured walk, meaning the dog is in a heel and under control. It looks like a dog on a loose leash, at the hip of their person. The dogs should not be pulling towards one another, or allowed to interact much at all. They may sniff the air, but keep a healthy distance between the two. Around 6 feet. I go around a mile during this time, it allows the dogs to become accustomed to each other without having to directly interact. Also, it can reduce some of the frantic energy from overly excited dogs.
When you return home, if all seems well, it is time to come inside. Each dog should remain on leash inside the house, and be allowed to settle before removing the leash. Once both have relaxed and are calm, then let go of the leash. If the dogs choose to interact, fine. If they choose to remain calm and resting, also fine. Do not force interactions here. Now, they can drag the leash behind and meet closely. With the dogs still attached to a leash, I can regain control if necessary. The leash can come off if all is well. If all is not well, use the leash to control the dogs ability to be near one another, keep them separate but in the same room. You may have to repeat this process over a few days.
To make introductions go smoothly, a good heel is important. Without a solid heel, the walk quickly becomes chaos as the dogs pull towards one another and desperately bark louder and louder. As in many things, the training prior to an event is the most important piece.
This process works for dogs without behavioral issues. If your dog is aggressive, nervous, or reactive it is best to consult a professional prior to attempting introductions.