Instructions
Venture to Nibelheim, a town due southwest of North Corel. In Nibelheim, there is a house called Shinra Mansion, where Vincent lies in a coffin in a basement cavern. The door to the cavern is locked, and the key is not so easily obtained. Find Shinra the mansion and walk upstairs to begin searching for the key.
Make your way to the top floor of the mansion and look around until you find a safe. You will need to enter the combination in less than 20 seconds if you wish to open it. There is a way to investigate and figure out the combination for the lock, but for those who simply wish to hastily obtain Vincent, the combination is provided here. For those who don't want a spoiler, turn away now and begin your search. (The combination is right 36, left 10, right 59, right 97.) Be prepared to fight--you will subsequently be attacked by a boss called Lost Number.
Prepare yourself for somewhat of a challenge during this battle. Lost Number is divided into two halves, one that is weak against physical attacks and one that is weak against magic attacks, being red and purple, respectively. You'll be glad if you still have Aeris with you at this point in the game. Her level 1 Limit Break, Seal Evil, will prove efficient, as it will paralyze Lost Number for a good amount of time, enough for you to significantly reduce the boss' HP. Continue casting Seal Evil when her Limit Break reaches maximum, and you shouldn't have too much difficulty bringing Lost Number down. For winning the fight, you are given a level 4 Limit Break for Red, called Cosmo Memory, and you will find the Basement Key in the safe.
Head back down to the basement and unlock the door. Beyond it, at the center of the room you'll find a coffin, where Vincent lies. Press the circle button and Vincent will rise and ask a question. Respond by mentioning Sephiroth; he will lie down again. Talk to him one more time, and you'll need to ask him what his name is.
Return to the main entrance to the basement cavern. Vincent will be standing there and will tell you he has decided to join you.