This is fairly simple, it is just choosing the right responses to her.
When talking to Yuffie this is what you have to say:
1. Not interested
3. Wait a second!
4. That's right
5. Lets hurry on
She is easy to find, just run around in the world map and inside the forest areas, soon you will encounter her, just win the fight and choose the above responses and she will join :)
Edit: As mentioned by TheGreatKoala you will not encounter her till after the Mythril Mines.