Summarize:

Trade with a friend or migrate them from Pokemon Ruby, Sapphire or Emerald version. You will not be able to fight Regigigas without them. You should also have: A strong Pokemon (Preferably Breloom or Parasect) 40+ Dusk balls When you approach the statue, he will awaken and you can fight him. He is strong but has the Slow Start ability, so use your first five moves to lower his attack and speed stats. Make sure you save before fighting. If Regigigas blacks you out, you run out of balls, or you kill him, you can just switch your DS off and on and try again. If you kill him and you haven't saved your game, you must defeat the Champion again so he will respawn.
Make sure you have Regirock, Regice and Registeel in your Pokemon party. Navigate to level B5F, where you will find the statue of Regigigas.