I know the theory, in that I trained Jas to lie down by putting him in a sit and then lowering a treat to the floor in front of his nose. It took him a few goes, but he got it fairly quickly. Problem is, the pup doesn't seem to want to keep his bum on the ground. He sits, gives the paw and recalls beautifully, but down is just not happening. He follows the treat with his nose and ends up with his nose on the floor and his arse in the air. I persevere, and he continues to waggle his bum around while wiping his face on the floor trying to get the treat. Or, he keeps his bum down, and his nose, but his front legs still straight. Huh. So, any tips?
I managed this by dragging a treat along the floor in front of the pups nose after she sat. Once she laid down I held her there and said 'good girl to lay down'. I only had to do this 3/4 times before she got it. Now my 'lay down' command just involves me dragging a finger along the floor. If she doesn't get it you could always just pick up her front legs whilst she sitting and put her there! Once she's in the position you want just keep repeating 'lay down'.
It's taken me two weeks to teach 'sit', 'lay down', 'off', 'no', 'paw' and 'come'. Now if only get the 'no biting' to work
Try this: sit on the floor with your knees bent making an arch. Sit your dog on one side of you. Offer a treat with the opposite hand and encourage the pup to come through your legs to get it. He will have to get down to get it. What sort of dog is he? Some dogs, especially deep chested ones, don't like getting right down, especially on hard floors, and need more effort to train. It this is the case, it might be worth starting to get the down on something soft. Good luck!