The command "off" means don't touch with your front paws. In other words, don't jump up. Before you correct your dog for jumping up, be sure that you have done thousands of repetitions of having him sit for a treat, with you and especially with other people. You will also need your dog to be able to do a sit-stay while someone walks around him. Start by having something that will entice your dog to jump up, such as a toy or treat. If he sits immediately, great! You've done your homework. If not, let him jump up as much as he wants and ignore him. As soon as all four feet are on the ground, give him the toy or treat. Once he is automatically staying on the ground, add the command "off."
Another way to teach "off" is with the leash. As someone approaches, warn your dog with the "off" command. If he launches himself into the air, give him a quick tug on the leash. Tell the person who is helping you not to pet your dog until he is sitting or all four feet are on the floor. You can also use "off" to correct your dog for jumping up on counters or furniture. Don't use the word "down" to mean no jumping. You have already trained him that "down" means something else. See chapter 8 for more information on dealing with jumping up problems.
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Fundamentals of Dog and Puppy Training. Although dogs shouldn't be attributed with having human characteristics, they are intelligent enough to be able to understand the concept of, and execute, certain actions that their owners require of them - if these actions are asked in a way that dogs find rewarding.