Most dogs like to play the game catching a flying disc, a agile dog may grasp that easily. However, you must be patient for other dogs, which need to be trained again and again, only in this way can the dogs learn how to catch.
At the begining of training, you can use a piece of cookie or beef jerky instead of a flying disc. Let your dog sit down in front of you first, then take out a piece of cookie or beef jerky, let your dog smell it, and take a few steps back. Facing to the dog, say "catch" to him, at the same time, throw the dog a piece of cookie, if the cookie drop in the top of his nose, most dogs can catch it, as well, let him eat the cookie as a reward.
If the dog can't catch it, you should pick up the cookie fell on the floor quickly, and throw it to him again. Don't allow the dog to eat the cookie, only when he catchs the cookie in the air. After training for some time, the dog will be aware of that you hope him to catch the cookie in the air, the puppy will master the skills of the game.
When your dog has had the ability above, you can train him using a ball instead of the cookie. At this time, the motive of dog is not the cookie, but in the game. You can let your dog stand up or sit down, hold a ball and say "catch" to him, then throw the ball to the top of him. As the dog has got skills of this game, in general, he may catch it well. After that, call the dog back to you and let him spit the ball, give him a little food as a reward.
Training the dog frequently, he will desire the game more and more, as well, the action of his catching will be more and more skillful, even he will often jump and catch in the air. If so, you should give him enough encouragement and tasty foods as a reward, which is very benefit to training.
Now, we can train the dog to catch when he is running, using a flying disc. At the begining of trainning, the speed of flying disc should be slow. Stand in front and right of him, throw the flying disc, say "catch" to him, most dogs will run quickly toward the flying disc, jump and catch it. If your dog can succeed to catch, reward him fully to improve the interest of dog. If the dog can't catch, repeat the training until he can. With ability to raise, you should change the direction and speed of the flying disc, to train his ability to catch.