Where do the put the animal's body after they put them to sleep?

They ask you if you want it cremated. Regardless of the answer, they can't give you a dog carcass back, so they burn it anyways. They burn all the dogs of the day at once, and if you want ashes, they give you a little bit of the huge pile of ashes (so it might not even be your dog). Some places will just burn your dog if you pay extra.