Defeat Lt. Surge and obtain the Thunder Badge
Progress through the main story until you can use Surf and Strength
Go to the Power Plant on Route 10
Save the game before encountering Zapdos
Bring a Pokémon with False Swipe or another move that leaves 1 HP
Bring a Pokémon with a sleep or paralysis move
Bring Ultra Balls and Timer Balls
Use False Swipe to lower Zapdos to 1 HP
Inflict sleep or paralysis on Zapdos
Throw Ultra Balls until Zapdos is caught
If Zapdos faints or escapes, reset and try again if you saved beforehand