Usually, it is a big deal for a dog to meet another dog. The only exception is when a dog has been raised meeting new dogs commonly, so that it becomes routine. The next best scenario is dogs that go through a socialization puppy class where they are allowed to wrestle and have full contact play. Preschool is where they learn proper manners (e.g. you don't jump on dogs bigger than you, unless given permission). Even dogs who have been through puppy preschool (2-5 months of age) need regular exercise meeting new dogs throughout the few years of life. An important period to meet new dogs (e.g. at daycare or the dog park) is between 1 and 3 years of age, since dogs develop emotional maturity by about 3 years old. If the dog is very experienced by this age, he will usually be dog-friendly for life unless some bad experience, or the owners unintentionally allow the dog to become controlling.

Even dogs who have been through puppy preschool (2-5 months of age) need regular exercise meeting new dogs throughout the few years of life.

Dogs who meet other dogs easily develop an outgoing friendly personality that allows them to make friends for life, play for hours, and get lots of exercise. (Sounds pretty good for people too!)

Meeting When Both Dogs Are On Leash While Out Walking
Proper dog etiquette is to ask the other owner if their dog is friendly with other dogs. They will usually know. If they say "yes", then ask if it is OK for the dogs to meet. If "yes" again, here is the secret: you greet the other dog first with a high happy voice, and relaxed body language. In this situation, you are acting as a leader, and showing your dog what you want. Move your dog behind you or step on the leash while you get low (don't loom over the other dog; it is a threat.) Offer your hand, while looking off to the side and let the strange dog make the first touch. This shows trust on the dog's part, by approaching you. If the dog freezes, it is showing you a threat; either stay there for a while, act relaxed and wait, or just back off and move on.

Your dog will likely be very interested and want to sniff, but only allow this if you sense a friendly attitude. Allow them to sniff, but continue to talk in a high happy voice, and praise your dog for friendly behavior. Beware of leash entanglement. If they begin to spin, pull your dog away and start over. Just when you pull your dog away is the most likely time they will get aggressive. Do it quickly and unexpectedly, so your dog doesn't have time to snap. If your dog does part friendly, the reward is another immediate visit to the same dog before moving on. Continue keeping the leashes untangled. Remember to act relaxed (even if you're not) and praise friendly behavior. They only way your dog will learn is by experience with your guidance. If your dog has been aggressive in the past, have your dog wear a muzzle for the safety and show your dog attacks don't work.

The ideal signal from either dog is a play bow (front legs slap ground, with rump up.) This signals no threat, and a friendly invitation to play. If either dog does this behavior, praise it profusely.

Meeting When Both Dogs Are Off Leash
As soon as you see the other dog, call your dog to you and put him on a leash. If it is too late, and you can see your dog is going to the other, start infusing the situation with high happy talk and encouragement to get along. Give your attention and praise to the OTHER dog. Call him to you if he seems friendly. Try to make friends with that dog while your dog watches and hopefully follows your lead. When you see the chance, get your dog on leash and leave since you cannot control the situation.

Meeting When Your Dog Is On A Leash And The Other Dog Isn't
In this case, just keep on moving and don't take a chance since there is no one to even try to control or influence the other dog. If the dog is very friendly, you may wish to stop and say hi.

Meeting When Your Dog Is Off Leash, And The Other Dog Is On Leash
This is a great opportunity to practice your COME Instruction. If your dog does not come to you under this situation, you should not let your dog off leash again until you have worked on COME. The way to do this is to use a long leash, and repeatedly call the dog, give short tugs if necessary, then treat and praise compliance. Finally let him off leash when COME is reliable, but initially have him drag it. Call him every few seconds. If he comes, he gets a longer time off leash. If he doesn't come immediately when called, run after him and step on the leash then start working on COME again.