Let’s get one thing straight from the start: “Down” means “lie down on the ground.” It is not to be confused with “four paws on the floor,” which we call “off.” Train all the humans who have regular contact with your dog to make this distinction and never to say “down” when they mean “off.” (Use different words if you want, but make sure you always use the same cue for the same behavior.)
As in teaching “sit” or any other position, the basic approach is to get the dog to go into that position, mark it with the clicker or “yes,” and reward the dog while still in position.
The hardest part is getting to “aha”—the moment when the light bulb goes off in the dog’s head: “Oh, that’s what she wants me to do!” It takes different dogs different amounts of time to learn different skills with different approaches, so be patient.
Once you’ve got the “aha” moment, seal the deal by practicing several successful repetitions and assigning a hand cue, verbal cue, or both.
The approach with “down” is very similar to the one shown in the “sit” video. With a treat in your hand, hold your hand flat, palm down and parallel to the ground. Move your hand down to the ground and hold it there till the dog is lying down. Mark and treat when he gets there.
Repeat until you get the “aha,” and then add the verbal cue “down” and a hand cue similar to the motion you used to get the dog down: holding your hand flat with your elbow at your side, move your hand downward from shoulder height to elbow level.
Another option, also shown in the “sit” video, is to physically force the dog into position. However, it will probably take longer for the dog to learn this way, because you’re delaying the “aha” moment. When the dog voluntarily gets into the position, and you mark and reward, he’ll get the idea much more quickly.
