Proofing is the final step in training your dog any new behavior. It involves practicing behaviors in a variety of situations with different levels of distraction. Failing to proof behaviors is the reason why your dog may perform behaviors well in your living room, but seem to forget all his training the minute you leave the house.
Think Like a Dog
To understand why proofing is important, you must first be able to understand how your dog thinks. Dogs aren't able to generalize the way people do. This simply means that your dog may understand what "sit" means when you give him the command in your kitchen, but he may not understand that it means the same thing at the dog park.
Imagine you are sitting at your dinner table, and your mother says, "Get your elbows off the table!" When she says this, you understand that this is the rule for all tables. You need to keep your elbows off this table and the table at your aunt's house and the table in a restaurant. You are able to generalize. If, on the other hand, you were able to tell your dog to get his elbows off the table, he would understand only that he wasn't allowed to put his elbows on this table. You would most likely have to remind him again at your aunt's house and at a restaurant. He is not able to generalize, so he does not understand that the rule applies to every table.
The same proves true for every behavior you teach your dog. If you want him to sit or down (or perform any other behavior) in every situation, you must first practice these behaviors in a wide variety of places. When your dog is able to perform a behavior on command as perfectly at the dog park as he does it in your kitchen, you can consider the behavior proofed.
Add Distraction and Different Settings
When you begin training your dog to do something new, you usually start off in an area that's fairly quiet with very low distraction. Once your dog is able to respond quickly to a command in this setting, it is time to add some distractions and new settings. Do this slowly, and work on adding one new thing at a time.
Let's look then at how you would proof a "down." Practice the down until your dog is able to respond to the down command fairly quickly. Then begin to slowly add new things. You can start by adding some distraction. Have another family member come in the room. Practice several times, and then turn on the television while you practice the down. Slowly add more distracting things to his environment - other dogs, running children, loud noises - while practicing the down.
Once your dog is able to lie down quickly on command with some distraction, begin practicing in different places - another room, the backyard, the neighbor's house. Keep each training session to about 10 minutes, and stay upbeat. If your dog begins making mistakes, go back to the last time he was responding quickly to the command.
After you have practiced a behavior with different amounts of distraction and in a variety of locations, your dog should have a really good grasp of the behavior. He should now be able to perform the behavior as well at the dog park as he does it in your living room. Once you've gotten to this point, the behavior is proofed!