I'll be talking about rewards in two main contexts: for going into the crate (more about crate training later), and for going to the bathroom outdoors. While praise, play, or other things the dog likes are never a bad idea, I'd also recommend using food rewards at least some of the time.
You should be especially generous with your rewards when your dog is first learning the behavior. So the first few times that they go to the bathroom outdoors, praise like they just won the Olympics and give them a treat. Later on, the praise can consist of a "good dog" or two and the treats can be occasional.