In Final Fantasy X every character has a celestial weapon. When you receive this weapon the "NO AP" ability is put in. To get rid of that you'll need 2 items, a sigil and a crest. When you want to get the celestial weapon first you must have a celestial mirror. Here are the locations of the weapons and the items.

¤ Tidus

The Caladbolg - Beat the chocobo trainer on the Calm Lands. Then the guard at the south of the Calm Lands is gone and then you can get the Caladbolg down there.

Items needed:
Sun Crest - Zanarkand Dome, where you fought against Yunalesca
Sun Sigil - Race against the chocobo trainer and set a time of 0:0:0.

¤ Yuna

Nirvana - Catch all enemies in the Calm Lands and bring them to the monster arena. A chest will appear and in there is Yuna's Nirvana.

Items needed:
Moon Crest - Besaid Island - Beach
Moon Sigil - Defeat every aeon of Belgemine at Remiem Temple.

¤ Auron

Masamune - To get Auron's celestial weapon first get the Rusty Sword at bottom of the Calm Lands (near the Cavern of the Stolen Fayth).

Items needed:
Mars Crest - Mi'hen Highroad - Oldroad, South
Mars Sigil - Capture 10 monsters of 10 different species in 10 different regions.

¤ Wakka

World Champion - To get Wakka's World Champion go to the café in Luca and talk to a woman, she'll give you the celestial weapon. (But you'll have to play Blitzball sometimes)

Items needed:
Jupiter Crest - Luca, inside locker in Auroch's locker room.
Jupiter Sigil - Offered as a prize in blitzball league matches, but only after Wakka has the Overdrives: Attack Reels, Status Reels and Auroch Reels.

¤ Kimahri

Spirit Lance - To get Kimahri's celestial weapon go to the Thunder Plains, there stands 3 stones that give some light, press SQUARE and you'll see the Spirit of the Cactuar being released. Do this by all stones, and then search in the first section for the Qactuar ghost. Follow him and you'll come by a rune. Press SQUARE there and a chest will appear.

Items needed:
Saturn Crest - Mt. Gagazet, columns after Seymour battle.
Saturn Sigil - Catch all butterflies in the Macalania Forest. Note that you must catch the blue, not the red!

¤ Lulu

Onion Knight - To get Lulu's Onion Knight go to Baaj Temple and go underwater and fight Geosgaeno, the boss that you encountered before. After you beat him search for a chest in that area.

Items needed:
Venus Crest - After getting the Airship, go back to the Farplane in Guadosalam.
Venus Sigil - Evade 200 times the lightning at the Thunder Plains without being hit. Then go the Al Bhed Travel Agency and open the chest there.

¤ Rikku

¤ Godhand - To get her celestial weapon enter the password "GODHAND" on the Airship. Then go to the new area, there you can open the chest.

Items needed:
¤ Mercury Crest - In a Sand Whirlpool in Sanubia Desert.
¤ Mercury Sigil - Complete the village of cactuars sidequest and look for a treasure chest in the sandstorm area.