Zapdos can be found in the Power Plant in the Kanto region. You must first start a quest by talking to the NPC just inside the Power Plant and complete it before Zapdos will appear.
If you accidentally defeat Zapdos, he will respawn in 7 days.Once you capture Zapdos, he will no longer respawn.
You can also receive a Zapdos Egg as an Ultra Rare drop from defeating the Legendary Birds Boss at Mt. Ember Summit on One Island.