How to get Yuffie

You can get Yuffie in two different spots. The first place is to go to the island where the Temple Of The Ancients is, or you can go to the small forests south of Cosmo Canyon. Once you are in one of these spots wander the forests until you get into a battle with a small girl (Yuffie). Defeat her and you will be taken to a screen of her laying on the ground. DO NOT GO TO THE SAVE POINT!, or else she will run away instead go up to her and talk to her. Answer her with choice 2, then answer the rest of the questions as if you aren't interested and ignoring her. When she says she is gonna leave answer "Wait a second!", and then she will say she will join you, and then choose "leave without asking her name" and she will run after you. And now you have Yuffie!

How to get Vincent

When you are in Nibelheim (anytime in the game) go to the mansion and go upstairs and to the safe on the left side. Put in this combination, Right;36 Left;10 Right;59 Right;97, but remember you have to enter this befor the timer runs out, or else it will not work. When you finally open the safe fight the Boss, which has 8,000hp, so be ready. After you kill him you will get Red XIII's level 4 limit (Cosmo Memory), and a key. Now go through the secret passage to the right of the stairs and down into the basement. Go to the first door on the left and use the key on it and enter the room. Open the coffin in the middle of the room and there lies Vincent. After a breif discution with him, he returns to the coffin and asks you to leave him be, leave the room and as you are leaving he will stop you and join your party. And now you have Vincent!