Yuffie is a playable character in the game, but it is optional to find and recruit her.
You can find her early in the game, after leaving Midgar and can be a very strong party member later on. She can be found as a random battle encounter in forests and is named "Mystery Ninja".
After defeating her, you are taken to a field where you will see a Save Point, Yuffie and your party. Do not use the Save Point! When you return from the menu, Yuffie will be gone, along with some of your Gil.
Talk to Yuffie to start a dialogue, selecting the correct answers will recruit her to your party. These answers also have a bearing on the dating mechanics .
These are the answers to recruit her:
Yuffie: "You spikeyheaded jerk! One more time, let's go one more time!"
Reply: "Not interested."
Yuffie: "You're pretty scared of me, huh!?"
Reply: "..... petrified."
Yuffie: "I'm really gonna leave! REALLY!"
Reply: "Wait a second!"
Yuffie: "You want me to go with you?"
Reply: ".....That's right."
Yuffie: "All right! I'll go with you!"
Reply: "..... Let's hurry on."