Here are the 7 Dragon Balls scattered throughout the Team Training world. Once you collect a Dragon Ball, it will be held in your "Key Items Bag" until it is needed later.
Once you collect all 7 Dragon Balls, you can take them to the Old man near Kami's Tower to summon Shenron (Lvl 60). After you summon him, you are allowed to catch him. Only hand in the DBs once you are ready to catch him, because you only have one chance to fight!
Where to Find the Dragon Balls
Dragon Ball 1
In the truck, in the port of RR Base. You need to cross the water to reach this area.
Dragon Ball 2
Behind a rock on an islet in Route 20.
Dragon Ball 3
In Mt. Moon, when you beat the trainer close to the cave exit.
Dragon Ball 4
In Indigo Plateau, just before the center.
Dragon Ball 5
In Capsule Corporation, after defeating Pilaf.
Dragon Ball 6
On Route 10, hidden near a tree. There is a row of trees, the ball is upwards.
Dragon Ball 7
On Route 8 in a corner over Rock Tunnel.
When you get them all, go to Makyo Town and talk to the old man near the tower so you can summon and battle Shenron (Lvl 60). Once you summon him, you lose the Dragon Balls for good and cannot collect them again, so this is your only chance to catch him.