This article is from the Training Your Dog FAQ, posted to rec.pets.dogs newsgroup. Maintained by Cindy Tittle Moore with numerous contributions by others.
Proofing is a method where you make sure your dog understands a command, _after_ you have taught the dog the command. It isn't fair to proof a dog on a command when he is still learning what it means.
For example, you teach your dog to stay. After making him stay in a relatively distraction-free environment, you step up the pressure. You throw balls up in the air and catch them, squeak toys, have someone stand near your dog and talk softly to him. If your dog gets up, gently put him back. If after doing this for a while, the dog still gets up, then you start putting him back less gently, i.e. taking your dog roughly by the collar and putting him back, escalating to picking your dog up by the collar so that his front legs come off the ground and VERY slowly putting him back in its place, escalating to picking the dog up by its skin so that him front legs come off the ground and VERY slowly putting him back. Some dogs get the idea more quickly than others; stop your correction when he stays down.
When your dog passes this step, increase the pressure by throwing balls all around him, bouncing them on the ground, etc. Also, someone else should try to offer him food, make strange noises such as clapping , barking like a dog, meowing like a cat, using toys or things that make strange noises.
When your dog passes this step, increase the pressure by putting him on a stay and having someone shout in a loud voice "ROVER, COME!" (do not use your dog's name), "OK", "DOWN" (if doing a sit stay). If at home, put him on a stay and go and ring the doorbell. It should take several months (6-8) to work through all of these distractions and care must be taken to not blow the dog's mind by putting him in a situation that he is not ready for or by never letting the dog "win" (i.e., successfully perform an exercise).
Always let the dog "win" on the last exercise in the session. That is, end the sessions on positive notes, with much praise. This keeps your dog interested in the work.