To get Yuffie to join your party, roam around a forest until you fight a girl called a "Mystery Ninja." Beat her, and you'll be taken to a screen with a save crystal. Ignore that and keep your eves on Yuffie. Talk to her and reply with the following answers: Not Interested, petrified, Wait a second, that's right, and Let's hurry on. You should now have Yuffie as a permanent member of your party.