What is the best way to play with your best friend? Play should always be considered training and training should be considered play. Interactive games that make you look like a trusted, respected friend are best. Retrieve games, hide and go seek, and tug of war are all great games. Here's a little information about each of these games:
All puppies can learn how to retrieve. What seems to be the most important thing is if they are interested in chasing and getting the object. The problem often becomes bringing the object back to you and dropping it for you to throw again.
Start in a small space (not outdoors) and have two equal value toys (two tennis balls, two squeaky toys, etc). Toss one of the objects a short distance. When the puppy chases and picks up the object, show him the other one and as soon as he drops the first object, throw the second object. Keep this up only a few times and quit before he gets bored. Pick up the toys you were using and put them away for now. These will be considered your toys that you let the puppy play with on your terms. In fact, every now and then take the toys down and play with them for a few minutes in front of the puppy. Then put the toys away. This will build his desire to have those toys and play with you. When you break those toys back out later, your puppy will remember the fun you two were having and you can continue growing the interest in this game.
Hide and Go Seek
This is a fun game that not only builds on your relationship but also helps to work on getting your puppy to come when called.
Later, when your puppy knows "stay" you can play this alone with your puppy. I actually still play this game with my full grown dogs and they love it. I put them in a "Stay" and go and hide somewhere and then yell, "Find me!". I can hear them running all around the house looking for me, racing to be the first to find me.
With a puppy that does not know stay, you will need some help. Have someone hold the puppy while you tell the dog to "stay". Then go and hide, but make it an easy spot at first, like just around the corner. When you are ready call the puppy or say "Find me". Let the puppy find you and throw a party when they get there! Don't forget to hand out treats for their efforts. After a while, make your hiding places more difficult. Also, you can play this outside in the yard or on your off-leash hikes.
Tug of War: The controversial game!
Yes, I play this game with my pups. This can be a great game and it will not teach your dog to be aggressive. I may not play this game with a new shelter dog that I don't know well, but there is no reason not to play it with a young dog. The rules just have to be yours. YOU decide when to play. YOU decide when it's over. Just like the retrieve game, the tug toy gets put away when you are done. If you are really uncomfortable with this game, simply don't play it.
To play: Take the tug toy and hold it right in front of the puppy's face and say, "READY?" Then "OKAY!" or "TAKE IT". Tug for a couple of minutes and then use a neutral voice and say, "DROP" or "LEAVE IT" and push the toy towards your pup while you pull your puppy towards you with their collar. Keep pushing the toy towards him until he tries to spit it out. Then hold the toy again and say "READY?" When YOU are ready say, "TAKE IT". After a while you will not need to pull your dog towards you and push the toy toward them. They will begin to release the toy on their own as soon as they figure out that this is a game that you are both playing. Remember, quit before your puppy is ready to quit and put the tug toy away. The toy is yours and when you take it out you are "letting your puppy or dog play with it with you.