Go to the area near Gongaga Town where the burned out structure in the forest is. Don’t enter this area with the reactor, stay on the World Map. Go and fight in the forests near this area. (Or in the forests near Junon). Eventually you will enter a fight with Yuffie. She is very easy to beat, and when you have won, you will find yourself on a field with Yuffie and your party. There is a Save Point in the corner but don’t use it as Yuffie will run off and nick some of your money. Also don’t go into the main menu. Talk to Yuffie and answer in the following way:
“You spikey-headed jerk! One more time, let’s go one more time.”
“You’re pretty scared of me, huh!?”
“I’m really gonna leave! REALLY!”
Wait a second.
“You want me to go with you?”
“All right! I’ll go with you.”
……Let’s hurry on.
You can name her, and you now have Yuffie on your team.