Getting Vincent:
Take the key from the safe that contained the Odin summoning materia in Nibelheim. After defeating the Boss, Lost Number, walk down into the basement. Open the door that was previously locked (right before you enter the room with Sephiroth). Talk to Vincent until you talk about Sephiroth, then leave the room and start to go back up to the Shinra Mansion. Just before you get away Vincent will come and ask if he'll meet Hojo, then he'll join hoping to kill Hojo.
Getting Yuffie:
Yuffie can found in a random encounter in one of the forest areas. After fighting her, do not pause or use the save point. Talk to her and answer her questions with the following responses.
Yuffie: "You spikey-headed jerk! One more time, let's go one more time!"
Answer: Not interested.
Yuffie: "You're pretty scared of me, huh?"
Answer: ......petrified
Yuffie: "I'm really gonna leave!REALLY!"
Answer:Wait a second!
Yuffie: "You want me to go with you?"
Answer: ......That's right.
Yuffie: "All right! I'll go with you!"
Answer: ......Let's hurry on.
