Tidus: in the Calm Lands. You must get a perfect time of 0 seconds on the chocobo race for the man then find the place where the man was blocking.
Yuna: the chest outside the Monster Arena. You have to capture every monster in the Calm Lands.
Auron: you will need the Rusty Sword which can be found stuck in the ground near the Cavern of the Stolen Fayth. Then go to Mushroom Rock and examine Lord Mi'ihen's statue. Insert the Rusty Sword there and a glyph will appear, examine it and you'll receive the Masamune.
Wakka: Talk to the bartender at the Cafe in Luca. If you've won enough Blitz Ball games, you'll receive the World Champion.
Lulu: You can get the Onion Knight from a chest that is underwater outside Baaj Temple.
Rikku: put the password GODHAND in the airship.
Kimahri: go to the Thunder Plains and examine 3 Cactuar Stones A Ghost Cactuar will appear. Now go to Thunder Plains South, then a bit northeast from the save sphere. When you see a fallen lightning rod tower examine it to receive the weapon.