But if you use a toy for training instead of food, I'm confused as to what you actually do with the toy
do you give it to the dog, or what? 
When my greyhound comes home (he's in foster at the moment) I'm going to attempt to teach him a couple of basic things, and he isn't really motivated by food, but he has 1 toy that he absolutely adores that I could use as his reward.
So I guess what I'm asking is, how do I train with a toy?