Take your submarine and take it near the docking area close to Gold Saucer. Dive and there should be a underwater passage, pass through it and then you'll surface in a valley where a waterfall blocks a cave. There is another way to enter the cave, that is locate it on the map (its practically in the center of the world) and use a Green or higher Chocobo to climb up the mountain. Make sure you have Vincent in your party, and then enter the cave under the waterfall to view a scene. It'll clear up some things concerning Vincent's past.

Leave the cave and re-enter to gain Vincent's Level 4 Limit Break Manual, Chaos, and his ultimate weapon, Death Penalty