Vincent is found in the Shinra Mansion in Nibelheim. He is behind the locked door in the mansion's basement. To acquire the key, you need to open the safe on the top floor by entering the correct combination of numbers. These can be found around the mansion, by following the hints on a piece of paper found in the bottom-left room on the screen when you first enter the mansion.

The correct combination is right-36, left-10, right-59, right-97, and when scrolling through the numbers you can't go past them or it won’t work, so slow down when you near the numbers. You only have 20 seconds to enter the combination. You then have to battle the boss 'Lost Number'. Upon defeating the creature, you will receive the basement key and the Odin materia.

Then enter the room in the basement and find Vincent, who is resting in the coffin in the center of the room. Talk to him until he refuses to speak to you again, then try to leave the mansion. Vincent will join your party.