How do you get the griseous orb?

In Pokemon Platinum you can get it by going to the distortion world from Turnback Cave.

In Pokemon Heartgold and Soulsilver, the only way to get it is to bring an event Arceus to the Ruins of Alph and trigger the event. Then, when you have to choose between Dialga, Palkia, and Giratina you must pick Giratina.

Side note: You cannot trade the orb because if you have a Pokemon holding it while in the union room, it will instantly go back to your bag. The game creators did this because the griseous orb is not in Pokemon diamond or pearl.