Things You'll Need
Instructions
Travel to Lake Valor, which is to the west of Sunshore City and to the northeast of Pastoria city. If you are having difficulty finding Lake Valor, consult the world map (see Resources).
Approach the water at Lake Valor, and then press "Start" to open the main menu. Select "Bag" and press "A." Select "Surf" under the "TMs &HMs" menu. Surf to the exact center of Lake Valor, where you will find a cave. Disembark outside the cave and save your game. Saving your game is crucial, as it may take several attempts to capture Azelf.
Enter the cave and approach Azelf. After a brief dialogue, you will enter into battle.
Cast Sleep on Azelf to weaken him and to prevent him from using his Nasty Plot ability. Once Azelf is asleep, throw Dusk Balls at him until you catch him. Dusk balls have a catch rate of 3.5 and will only work in dark conditions and environments. Since you are in a cave, the conditions will always be considered dark and you'll be able to use Dusk Balls inside of it.