To get Yuffie, search the forests around Junon and Fort Condor, and sooner or later you'll run into the "Unknown Ninja". Beat her and the screen will change to your attack party and Yuffie. (DON'T open the menu or use the save point or she'll run away with some of your money) Talk to her and answer her like this:
Yuffie: "You spikey-headed jerk! One more time, let's go one more time!"
You say: Not Interested.
Talk to her again.
Yuffie: "You're pretty scared of me, huh!?"
You say: ......Petrified.
She'll start to walk away but...
Yuffie: "I'm really gonna leave! REALLY!!"
You Say: Wait a second!
Yuffie: "You want me to go with you?"
You Say: That's right.
Yuffie: "All right! I'll go with you!"
You say: ......Let's hurry on.
Name her whatever and there you go. You now have Yuffie in your team!