How do you open the ruins on six island?

The ruins are on Seven Island. You need to go to a cave with a boulder puzzle. You need to put the boulders in the right places so that the ruins can be accessed. When you have the boulders positioned, you will "hear" rumbling on the game and the ruins will be accessible, where you can catch Unowns.

If you are talking about the Dotted Hole on Six Island, then the way to get in is using HM Cut on the door. The Sapphire is inside that cave!