I found simply attracting the dog with treats in hand (sniffing, no taking), going to the mat and pointing down at the mat and letting a treat drop works. Do this a couple of times to get the dog to anticipate the treat at the mat place, then get the dog so he's all the way or most of the way on the mat and drop the treat. From there, bringing my hand down to the mat so the dog is encouraged to lie down for the treat. Introduce the verbal cue about half way through these steps. When I point at the mat from the middle of the room and say, "Rover, place", I want him to run to the mat and await my treat, which I would probably toss to the mat. If he'll stay there for a couple of seconds, I'll toss another treat, and another. I'll put a toy on the mat when he's out of the room to get him to investigate the mat, no so much stay there yet; like baiting the crate. I'll work on going to the mat with treats several times in the course of an evening, but not expect him to totally get it for a couple of days. As to chewing on the toy on the mat, that comes later. I'd give him the toy, then point him to the mat. Praise madly when he goes to the mat.
