It's the same as catching any other Pokemon, but just requires more patience. Here are a few tips I would recommend for catching Regigigas:
Bring along a Pokemon to fight it that can resist or nullify its attacks. Regigigas' moves at Level 70 are Confuse Ray, Stomp, Revenge, and Zen Headbutt. Having something like a Mismagius or Honchkrow on hand would be helpful. the best Pokemon to use would be a Ghost/Dark type like Sableye or Spritomb, but really, just bring along your best Pokemon (obviously).
Make sure you pack the appropriate Poke Balls. Bring lots of Ultra Balls, and make sure you also pack Timer Balls, as they'll become very potent capturing tools later in the fight. I forget if Regigigas is fought in a cavern or not, and if so, you could even bring along some Dusk Balls! The more Poke Balls you have with you, the greater your chances are of catching it!
Its ability works against it, so use those 5 Slow Start turns to lower Regigigas' HP or put a Status Ailment on it, since its Attack and Speed will be cut in half for the first five turns of the battle.
Save your game progress right in front of it. Unless you're lucky, Regigigas likely won't be captured the first time you fight it, even with all of of those Poke Balls, low HP, and Sleep or Paralysis inflicted. Save your game right before you fight it, so that if you fail to catch it, you can just reset your game and try again!
I guarantee you'll capture it if you follow these steps, or even if you only follow the last step. All it takes is a bit of patience and the luck of the draw.
