Yuffie Kisaragi: In order to get Yuffie on your team you will need to continually fight monsters in any forest once you leave Midgar. Eventually you will encounter Yuffie in a fight, after you defeat her you will go into a separate area only available after this battle. You will need to answer the questions she asked correctly in order to gain her as a member of your party. The conversation should go like this:
Yuffie: You spikey-headed jerk! One more time, let's go one more time!
Cloud: Not interested.
Yuffie: You're pretty scared of me, huh!?
Cloud: ...petrified.
Yuffie: I'm really gonna leave! REALLY!
Cloud: Wait a second!
Yuffie: You want me to go with you?
Cloud: ...That's right.
Yuffie: All right! I'll go with you!
Cloud: ...Let's hurry on.
NOTE: Do not press triangle or go to the inventory screen as this will result in Yuffie running away.
Vincent Valentine: In order to get Vincent on your team you will need to go to the Shinra mansion in Neblehiem (This can be done the first time you go here). Go to black safe in the top left of the mansion and enter this code in the time provided: "Dial 1: Right 36, Dial 2: Left 10, Dial 3: Right 59. Dial 4: Right 97". Opening the safe you will fight a boss monster which is reasonably easy to defeat. After the battle you will acquire a key from the safe which opens a door in the basement to a room where Vincent is sleeping in a coffin.
