This requires careful observation, lots of gates and pens and time for slowing down interactions. Too often, especially for example at dog parks, people seem too eager to let their excited dogs play together. You might want your dog to burn off steam, and you have just half an hour to do it, but this is not a good way to teach dogs good doggie manners, and it's not fair to other dogs who might not want to be immediately ravished by a complete stranger-dog. If a dog gets scared and starts screaming while being ravished (or more typically, a dog might start screaming at the very thought of being ravished), this can provoke prey aggression in even an ordinarily friendly dog. Dogs shouldn't be forced to play before they are ready.

My aim is to wait until the dogs learn how to be calm together, to give them a chance to get to know each other, before I let them play together. Many people can't tell the difference between playing and fighting, happy or nervous, friendly or aggressive behaviors. Imagine if a stranger is walking down the street, suddenly sees you and runs across the street to give you a big fat hug! Is that friendly? No, it's actually aggressive. If your dog is dragging you down the road to sniff another dog, this isn't friendly behavior [0], it's rude. And unfortunately, when the dog your dog is dragging you towards starts barking, "stay away!" that dog is ruled unfriendly, but really, it's understandable. Your dog might not intend to be rude,  but you were teaching your dog that it's okay to go hug strangers.

Just as some people are shy or socially discombobulated, dogs also vary in their ability to send or receive socially astute messages. To teach dogs polite manners, the only thing necessary is to think like your kindergarten teacher. At first, everyone keeps themselves in their own spaces. I don't allow friendly dogs to pummel other dogs. You can learn a great deal by observing interactions between dogs that are separated by a fence. If they sniff and wag politely, if they BOTH seem eager to play together, if their body language is rounded and soft, and especially if their size and weights are compatible, then whoo hoo, let them have a field day, first in a small space, and then (as they demonstrate continued soft, controlled play) in a larger space.

But if one dog is showing predatory behaviors -- that is staring, with a harder facial expression, eager to pounce on a dumb clownish dog -- then I'd wait on that one! In fact, any time play seems to escalate or get at all panicked (I often begin indoors), then one of the dogs isn't really being friendly, but is falling into a predatory game (treating the other dog like it's a bunny wabbit), and you have to stop the game.

Similarly, if one dog is insanely driven to play and the dog on the other side of the fence is completely ignoring it, the polite thing does NOT involve releasing the insane-to-play beast onto the I-only-vant-to-be-left-alone dog.