How to Unlock Yuffie/Get her to join your party - FF7
Yuffie is the first optional character that you can pick up in Final Fantasy 7 and you can find her early on in Disc 1 after you complete the Mythril Mine, in the area right before Junon. To trigger the battle encounter with Yuffie you'll want to run around in forested areas and fight enemies here.
Around Junon you only have a 10% chance or so to encounter Yuffie each time you get into a battle and that chance increases the further through the game you get. The battle with Yuffie isn't challenging at all, she's always weaker than the enemies around her.
Once the battle is over you'll find yourself in a unique area with your whole party and Yuffie standing around (pictured below). DO NOT USE THE SAVE POINT! It's a trick. If you use the save point or answer wrong when talking to Yuffie she'll steal your gil and flee from the area. If this happens you'll have to fight enemies in forests again until you encounter her.
Below is a list of the five correct answers that you will want to give Yuffie when she confronts Cloud. If you answer her correctly all five times she will join your party - it's as simple as that!
1. "Not Interested"
3. "Wait a second!"
4. "That's right"
5. "Let's hurry on"