Most dogs like to jump up on friends and family, and most owners have to train their dogs to keep all four on the floor, especially during greeting times. There are a lot of different methods out there for eliminating this problem behavior, but some of it is unnecessarily harsh or complicated, and the harsh methods sometimes backfire. I've worked with dogs whose owners put e-collars on them and shocked them hard when they jumped on company. Methods like that are a recipe for disaster, and you often end up making the dog skittish and upset without doing much about the jumping.
Here's the understanding I favor for dealing with problem behaviors in general and for jumping in particular: dogs do what they practice, and they do what's rewarding. The more times a dog repeats a behavior, the more likely he is to do it in the future, and the more the behavior is rewarded, the more likely he is to choose it in the future. So if we practice things with our dogs and make them rewarding, the dogs learn to do them.
The flip side of that principle also helps us identify the source and solution to problem behaviors. If the dog is doing something you don't like, it's because that behavior is somehow getting practiced and rewarded. So you can reduce problem behaviors by preventing the dog from practicing them and getting rewarded for them. Improvement comes even faster if you can practice and reward an incompatible behavior.
For example, if your dog jumps on company, he's doing it because it's rewarding and because he keeps getting the opportunity to do it. Eliminating that undesired behavior means stopping him from practicing it and stopping him from getting rewarded when he does it. Teaching him an incompatible behavior, like sit, can accelerate the process.
Jumping is usually a prosocial behavior, a behavior intended by the dog to promote social interaction with the jumpee. Your dog is trying to play in order to greet and bond. He's trying to get closer to the face of the human or to check out whatever the human might be holding. It's quite counterintuitive to him to stay on the floor and wait for the human to greet him, so it doesn't seem sporting to me to punish the dog for being inquisitive and social.
As humans, we typically want the bond, but we typically don't want a dog who jumps or mouths because that can be frightening or even dangerous. Jumping is very cute when a ten-pound puppy does it at ten weeks old, but when a sixty-pound adult dog does it, he risks ruining people's clothes, scaring people who don't know he's friendly, or even knocking over a fragile person.
If the dog jumps up and people start hollering and the jumpee pushes him, you may be accidentally rewarding him. The yelling means a lot of extra social energy, and the pushing is a cross between getting petted and playing. So don't do it. He wants social interaction, and he needs to show an appropriate behavior in order to get it. And don't use a method that hurts your dog, like stepping on his feet, hitting him, or shocking him. He's trying to play, and it's poor form to punish him for it instead of teaching him how to play appropriately.
So with jumping, you need to remove the opportunity to practice it, and you need to be sure he doesn't get a reward for jumping when he does it. Since it's a prosocial behavior, the first step is to show your dog that jumping backfires and doesn't give him the continued social interaction he wants. When the dog jumps up, remove all attention, energy, and excitement from the situation. That means looking away from the dog, being quiet, and keeping your hands off him. Turn sideways, fold your arms, and look up and away. Face a wall if you can so he can't come around front to jump more. Teach him that jumping makes humans boring. You're not just ignoring this behavior; you're nonrewarding it very precisely.
When he offers a different behavior that's appropriate, like keeping all four paws on the floor or even sitting, come back to life. You're rewarding him for showing appropriate behavior, and non-rewarding him for inappropriate behavior. Sometimes when you come to life, he'll jump again, so go back to being a statue. After a few repetitions, it'll start to click with him that the jumps are backfiring, but the polite behavior will get him what he wants.
As you try this, be aware that getting rid of an existing bad habit sometimes involves an extinction burst. When the behavior stops working, the animal will sometimes try it even harder for a short period. Just think of it from the dog's perspective: for a long time, the jumping has been working to make the people interact and make noise. When all of a sudden it stops working, the dog might try a jump, then try another, then try a whole series of more intense jumps. Why isn't it working!? This kind of burst can lead people to abandon a technique, right as it's about to work. If you abandon it right then and go back to yelling at the dog, you've taught the dog to be even more intense. He's just learned that the reason it wasn't working briefly was because he wasn't trying hard enough. So take extinction bursts for what they are: a sign that the behavior is about to improve.
If you're serious about tackling this problem, make sure to train the humans the dog is interacting with. If some are carefully nonrewarding him for jumping but others are yelling, pushing, or playing, that's going to undermine the dog's progress.
What if you are careful to nonreward your dog but he keeps jumping anyway? With some dogs, especially young ones who have not practiced a pattern of jumping, it's enough to be a boring statue for a few seconds and to reward a polite sit a few times. However, with dogs who really like jumping or with dogs who already have a confirmed jumping habit, the jump itself can be a reward, so removing the social interaction isn't always enough to break the pattern. It may be rewarding enough for some dogs simply to get closer to your face or to go through the fun athletic exercise of bounding up and down. In these cases, ignoring it isn't enough.
Another common scenario involves a confirmed jumper is simply too active to wait out. If you have kids or an elderly family member, or if your dog is scratching at you as he jumps, it can be unsafe and painful to try to just wait him out, especially through an extinction burst.
So if ignoring isn't decreasing the behavior, and you're absolutely sure you're not in an extinction burst, adapt the method. Try leashing the dog during greetings, and step on the leash so he can't jump. A six-foot leash is long enough to drop a loop down to the floor and step pretty quickly. If you do this, be sure the dog doesn't have more than an inch or two of slack. He can get hurt leaping upwards if he gets some momentum before he hits the end of the leash. You also don't want to give him too little slack and create downward tension. You still need him to feel rewarded when he's choosing not to jump, and being pulled toward the floor is definitely not rewarding.
Once you have the right length of leash between your foot and the dog, the greeter should ignore him while he's attempting jumps and interact with him when he chooses to keep all four on the floor. If he sits, try to give him enough slack to do so. When he's doing something right, you should try to keep tension off the leash and to reward him with attention or a treat. Set him up so you can prevent him from practicing the undesired behavior, but also set him up so you can catch him doing it right.
Regardless of whether you just need to ignore a little or whether you need to use the leash, make sure to teach your dog a rock-solid sit. I've already gone over some methods for teaching it, and if you consistently practice and reward the sit with your dog in lots of situations, you can use it as a behavior that's incompatible with jumping. If your dog has a strong sit, you can ask him to sit when he starts to jump. Reward him when he sits. If you have a strong sit trained, you can use it instead of a leash for habitual jumpers. If the sit's not quite strong enough, it won't work, so if you find yourself repeating "sit, sit, Baxter, sit" at your jumper, your sit's not strong enough for the situation, so don't weaken it by nagging a dog who's not obeying.
Between carefully applied ignoring, using a leash to prevent practice, and using sit as an incompatible behavior, you should be able to train away problem jumping pretty quickly. If it doesn't seem to be working for you, leave a comment with your issue and I'll try to figure it out with you.