How do you get Yuffie?

To get Yuffie you need to answer each of her questions right otherwise just like you said she will steal your gil and run away. So the answer to her first question is "not interested", the answer to her second question is "petrified", the answer to her third question is "wait a second" and the answer to her fourth question is "that's right" and the last option you need to choose is "lets hurry on". Do not use the save point in the area either.

All you do is go into a forest usually by the big tower thingy with the bird on top and just keep going through the forests until you kill her she will get all ticked off blah blah you wake up in a place with a save point and whatever you do don't save she will run away she will ask you for a rematch you half to say not interested then she will say oh you're scared or sumpthin like that and say petrified then she will say come on fight me I think you say wait then thats right blah blah then say hurry on oh and at first she will be on you're party then I think she steals materia and then she leaves for a wwhile then latr she rejoins the party

inuyasha3
final fantasy rules! ! ! ! !

What do you do if you accidentally use the save point? Where does she go?

Go into a forest near Junon on the world map and get into random encounters. Eventually you will battle a Mystery Ninja. This is Yuffie. Defeat her and you will be taken to a scene with her and a Save Point. Do not use the Save Point. Instead, talk to her She will challenge you to a rematch, respond "Not interested." She will then ask if you are scared of her, respond "Petrified." She will say that she is going to leave, respond "Wait a second." She will ask if you want her help, respond "That's right." She will accept, respond "Let's hurry on." You will then get a name screen for her, and then she is your party.