In order to summon Shenron you must collect seven Dragon Balls in story mode. These spawn after each main story mode battle and can be found easily when playing as characters with the Dragon Radar. These are typically the "good guys" such as Goku, Krillin, Gohan etc. They can be identified as small green dots on the radar, different from the blue and red dots which represent battles. After gathering all of the Dragon Balls, press square and go to the capsule house. Scroll to the right and select the Dragon Balls, if you have all of them you should be able to summon the dragon by pressing X.