When a dog jumps on a human of its own free will, it is not "greeting" the human, it is asserting its dominance over the human; it is the dog communicating that it is alpha and/or wishes to own/control the human. A subordinate would never dream of running over and jumping on the alpha dog of the pack. Space is respect and lower members of the pack respect the higher members. If your dog jumps on humans, it does not respect them. Note: when a young puppy jumps on humans it is sometimes its attempt to reach one's face. Puppies need to be taught not to jump up on humans as this behavior will manifest into other meanings as the puppy grows up into an adult dog.
1. Do not let your dog make a big deal out of your arrival home. In fact, as the alpha leader of your family's "pack", you shouldn't even greet him or her for at least 15 minutes. If your dog jumps around and pesters you before that, squirt him with water pistol or shake a can filled with pebbles. This will startle him, and if done on a regular basis, calm him whenever you get home. He won't make such a big deal of your arrival, and thus learn that he can greet you without jumping. Follow the same technique for any visitors to your home. Do not introduce the dog to your visitors until after 15 minutes or longer.
4. Use the "Sit" command. This is one of the most basic, and important, commands. As such, if your dog is well trained, he will respond to the Sit command before even thinking to jump. If he does not respond well to the Sit command, then more training is necessary, as this is the foundation for dog obedience training. Train him until he responds to it in everyday situations, such as greeting and going for walks. The better he understands the Sit command, the much less likely he is to ever jump at all.
Why do dogs jump up? A plausible explanation arises from their ways of communicating with each other. A puppy greeting an adult dog often licks the adult’s muzzle -- a polite, deferential behavior. Dogs, of course, descend from wolves, among whom muzzle-licking is how pups get the grownups to regurgitate food for them. Domestic dogs rarely nourish puppies this way, but muzzle-licking has survived, maybe because deferential behaviors are handy for a social animal. Think of humans saying “No, after you.” Muzzle-licking is also an appeasement behavior -- something you trot out to de-escalate a fight. A human might lift up his hands, palms toward the person he’s arguing with.