Overdrives:

Auron: Find different Jeckt Spheres laying about the world. Some of these will give Auron a new Overdrive. In order to get Auron's final overdrive, you must find all ten.

Kimari: Use the Dragon Sword, which ability to drain HP and MP from the enemy. If the enemy has a Blue magic skill that Kimari can learn, he automatically will gain it . The most difficult Sunshine", which is obtained from the Omega Weapon. 

Lulu: Rotate the Right Analog-stick clockwise as fast as possible. The number should go up the more you rotate it. The more you level up, the easier it will be to cast multiple spells. 

Rikku: Rikku's overdrive combines items to create special attacks and power-ups during battle. Choose any two items to combine but two of the same kind will work. 

Tidus: Just keep using them over and over. After a while, he will learn his next Overdrive. 

Wakka: You can win new overdrive roulette (slots) types in the Blitzball Ranking and Tournament modes.