Teaching the "Out"
The "out" command tells the dog to let go of something he is holding in his mouth. He might have a toy that you want to take from him, he might have the remote control, he might have your best pair of dress shoes. He is enjoying whatever it is he has, but you need him to let go of it.
To train the out, you need to have something he will take hold of, such as a ball or a rope toy. You also to have some super yummy treats. Give him the toy, play with him, let him enjoy it for a minute or two. When you are ready, tell him "out" as you show him a treat.
When he lets go of the toy to take the treat, praise him. As soon as he finishes the treat, give him the toy again, so that he doesn't think that "out" means the end of play time.
If your dog plays keep away with his toys, where he runs off, keep long line on him so that you can reel him in to you. When he learns that you have yummy treats for him, he will be less inclined to play his keep away game. Also if coming to you with his toys doesn't always mean the end of play time, he will soon be happy to come to you with them.
You should practice the "out" with your dog three times a day, having him give you his toy in exchange for the treat three to five times each session. Soon he will release the toy quickly. At this time, you can begin to fade out the treats, and use the toy itself as his reward.
Teaching the "Leave It"
Leave it is a valuable command to train. It tells your dog not to pick up things that he shouldn't. It stops him before he has an undesirable object in his mouth. Maybe he's spying the electrical cords as if they are snakes that he must eliminate. Maybe he's preparing to chase the cat. Or he might be about to feast on some discarded litter as you take him for a walk. Instructing him to "leave it" tells him not to engage in a behavior before he begins.
To begin training "leave it", take a treat that your dog likes. Hold your right hand out flat, palm up, fingers together, with the treat on your hand and let the dog see it.
As he reaches for it, close your hand into a fist so he can't take the treat, move your arm away, and say, "leave it". Repeat three to five times, always using the same hand. Now put the treat in your left hand, and tell him your release word. If you don't already have a release word, I recommend the word "free". Allow him to have the treat. Practice this session three times a day, until you see that he is not looking for the treat in your right hand.
Now you can place the treat on the floor in front of the dog. Put the treat about a foot or two away from him. A treat directly under the nose is far too tempting at this stage. Have another treat in your left hand. If the dog attempts to eat the treat off the floor, quickly pick up the treat in your right hand, as you say "leave it". Again, repeat this three to five times and then give him the treat that you have in your left hand.
Once you see that the dog is not looking at the treat on the floor, you can begin to add a second treat on the floor, and you can begin to move the treat so it is in front of him, next to him, behind him. Gradually you can move the treat closer to the dog. Be sure not to rush, though. If he happens to get a treat he wasn't supposed to have, don't make a big deal about it, and back up a step in the training. When the dog is consistently not going for the treats on the floor, you can begin to fade out the treats from your hand.