Here is how I got Layla to do "down" from a standing position. I'd put a treat between my thumb and forefinger and hold it right against the ground in front of her while she's standing. First instinct is for her to go down on her front paws to try to grab the treat. She would sometimes start licking at it, but I still wouldn't give it to her. I'd repeat the "down" command and before long she'd lower her back half too. As soon as that butt touched the floor I'd click and let her have the treat. They understand "sit" means butt on floor, but the tricky part is knowing that down means butt AND chest on floor. So if you can get that chest down first, it goes easier
Now everytime I tell her "down" she automatically puts her chest down first and then her butt. I hope that helps!