First, defeat Broly in Story mode. He appears a few times in the story. Complete the Buu Saga, then search for Broly. He can be found hovering around the area where you collect Parallel Quests, in between there at the World Tournament area. Fly close to Broly, and he will attack you. Defeat Broly, and you will return to Conton City. Refresh the city to make Broly available as an instructor. To refresh the city, you can either do a quick mission or just create a Parallel Quest lobby and leave to load back into the city. Note: You must be "God" rank before you can train with Broly, as he does not appear before that.