Instructions
Travel to Twilight Town in the Gummi Ship. A couple of areas in the town have the creatures that you need to kill for twilight shards.
Go to either the Underground Concourse or Master Yen Sid's Tower and kill the nobodies called Dusts and Gamblers. Dusts have a 10% chance of dropping a twilight shard, while Gamblers have a 12% chance. You can access the Underground concourse by landing at the Usual Spot and going though the exit marked "3" in the Back Alley. For the tower, you can land at the Entryway and make your way up the stairs or start at the Sorcerer's Loft and go down to find the nobodies.
Buy twilight shards at the Moogle shops once you have acquired 30 or more. All the materials in "Kingdom Hearts 2" are available at the shops once you have retrieved a certain amount, except for the serenity materials.