At the font condor, turn around until you can see many bushes. Now head to the biggest bush with a hill behind. Fight a few battles in the bushes until yuffie turns up and fight you. After you defeat her, you will end up in a screen where yuffie lies there. You would notice there is a safe point. Don't save or else yuffie will take this chance and run away. Talk to her and she will drop some questions. When she ask for a rematch, say "Not interested". When she asks you if you are afraid of her, say "petrified". When she says she is going to leave, say "wait a second". When she ask you if you want her to join your party, say "that's right". When she ask you if you want to know her name, say "let's hurry on".