You may or may not get them upon finishing the game. It's all up to you. Now, how
to get them:

Yuffie:
Walk around any forest in the world map on any disc. Eventually, you will fight
an enemy called Mystery Ninja. If you're having trouble finding her, try
walking around the forests near Junon. She appears there very frequently. When
the battle starts, you will notice her awesome fire bomb-type attack. Bad news:
you can't use it once you have her. She will keep using this move over and over
until she loses. This battle is easy even at really low levels (she's at LV22),
since she only has 800 HP. When the battle ends, a scene in a grassy clearing
takes place. Your party is here with Yuffie, who apparently is dazed from the
battle. Do not use the save point here, as she will escape and you'll have to
find and fight her over again. She will ask for a rematch, but you know better,
so choose these answers in order:

- Not interested
- ......petrified
- Wait a second!
- ......That's right.
- ......Let's hurry on.

She will then join your party....no more rematch ^_^

Vincent:
He's at the Shinra Mansion in Nibelheim. You can get him in any disc as well.
First, you must get the Key to the Basement key item from the safe in the 2nd
floor (read Cosmo Memory Manual, Red XIII). When you beat the boss there, you
will receive the Cosmo Memory Manual, the Odin Materia, and the Key to the
Basement key item. Now, go to the mansion basement, and just before the door to
the laboratory/library below, enter the door to the north. Open the purple
coffin, and Vincent will pop out. The responses to take in this conversation
are:

- Talk about Sephiroth.
- Who are you?

Name him, and he will go back to the coffin. Try to leave the basement. When
you do, he will follow you and ask to join your party.