First go to the Shinra Mansion in Nibelheim and open the safe: Right 36, Left 10, Right 59, Right 97.

After have defeated the boss you receive a basement key. With it you can open a door below the massion. Go to the spiral stair case (the one hidden behind a wall, where a Shinra soldier said that Sephiroth 'disappeared'), and head towards the library. In the long, dark purple colored passage, which leads to the library, there is a door that your new found key will now open. Now you are in the crypt, move to the base, check the coffin and a mysterious figure will come out. Talk to him about Sephiroth, but he will not be in the mood. When he goes back into his coffin, open it again and ask; "Who are you?" You will call him a name and he will go back to sleep again in his coffin. Leave the room, and Vincent is yours!