Teaching your dog how to wave is adorable and it gives him an appropriate way to greet people. To perform this trick, your dog must raise a paw in the air while remaining stationary. You can teach him do this by using a combination of targeting and shaping. The shaping steps are :

1. Start with your dog in a sit/stay position and move a few steps away from him. Go back every few seconds for a full minute to reward your dog for not following you.
2. Standing in front of your dog, ask for his paw and click and treat him for giving it to you several times in a row.
3. Take a step away from your dog and ask for his paw. Click and treat the slightest effort to raise his paw without trying to move toward you. You may need to reward him for staying for a few repetitions before he'll remain in position and lift his paw.
4. As your dog raises his paw to place it in your outstretched hand, start fading this cue by removing your hand quickly. Click and treat your dog for swiping the air.
5. Repeat this step until your dog starts raising his paw when he sees your outstretched hand.
6. As your dog starts to offer swiping the air readily without moving forward, you can begin to verbally label this new behaviour as 'wave'.
7. Change the hand signal to an actual wave by changing the position of your hand from an outstretched palm to a waving hand. Offer the new cue (waving hand) right before the old cue (outstretched hand), gradually fading out the old cue until your dog is performing the behavior when you are waving at him.
8. Add in distractions and practice in new places until the bahvior is reliable.

Training involves many elements, but there are two things to remember. First, make the most of your dog's natural bahviour by combining it with tricks that you put on as cue, as the paw trick demonstrate. Second, teach your dog the bahviour you want him to perform, like sitting, in the presence of other people and other dogs.