My very favorite way to teach a dog out is when they are young puppies. It is fairly easy to get the out in a pup and highly rewarded it tends to stick with them for life. However, sometimes for various reasons that can't happen. In Teddy's case, when he was a puppy he had no interest in play. When his play drive kicked in later on he loved a strong game of tug and hated to let go of his toy. His out was looking like this...
He does not make one motion towards outing when asked. He values his toy too much. Now I have a problem. He won't give up his toy and he is a powerful adult dog now. There are multiple ways to teach an out. I could force it, but that will likely result in me getting hurt. I first tried trading him for cookies. This often works. When the dog brings the toy back they get a high value treat. They eventually learn good things happen when they bring the toy back. In Teddy's case he was guarding his toy while I traded the treat. He still wouldn't let me have it. It became a race to see if I could grab it before he could swallow his treat and get back to it. The next option I tried was two toy. Two toy seems to be his game of choice.
I take two identical toys outside for training. I throw one and keep the other. The toys have to be identical. If you use two different toys, they may have differing value to the dog. If they end up with the toy they value more then you still have the same issue. What I tend to find in highly driven dogs is that they will rapidly discard the first toy in the effort to get the second one. The one I have becomes the one of value. Here Teddy outs before I can even tell him to.
What sometimes happens is that the dog will drop the first toy a ways from the handler. I don't want Teddy to develop that habit so I won't accept it. He doesn't get what he wants (me to throw the second toy) until he does what I want (bring me the first toy.) Once he figures out what I want and provides back the first toy, he gets his toy and we are both happy.