This article is from the Final-Fantasy and other Square Soft Games FAQ, by firstname.lastname@example.org (Nick Zitzmann) with numerous contributions by others.
You can have Character #1 (Yuffie), join you during any disc. Go to
either Junon Area or the Gongaga Area and run around in the forests.
There is a slim chance that one of your fights will be against the
'Mystery Ninja'. Defeat her in battle, and you'll find yourself in a
field. Be careful when answering Yuffie's questions! If you mess up, or
if you try to save your game at a Save Point, she will escape and steal
some gil from you! Answer her questions in this order:
* Question 1: Second (lower) answer. ("Not Interested")
* Question 2: First (upper) answer. ("...petrified")
* Question 3: Second (lower) answer. ("Wait a second!")
* Question 4: First (upper) answer. ("...That's right.")
* Question 5: Second (lower) answer. ("...Let's hurry on.")
Yuffie will chase after your group when you are done chatting with her
and she will join you as a more or less permanent member.