To unlock Vincent Valentine for your party, first go to Niblehiem and enter the Shin-Ra Mansion. Battle and defeat the boss, Lost Number. The safe's code is right 37, left 10, right 59, right 97. Now go down to basement and talk to the center coffin (don't go the the library). Vincent will come out and talk to you about Sephiroth and after that, he'll return to sleep. Wake him again and get him to tell you his name and he'll go back to sleep. Head towards the stairs and he'll join your party.