You can get Zapdos at the Power Plant close (I don't know the exact location,but I have caught Zapdos) to the Cerulean City (where the water type gym is) You can catch it by: using a master ball or lowering its health down and throwing a great or ultra ball.(the chances are very slim when trying to catch it with a normal Poke ball, but my friend has done it before.) Try not to kill it, because it may not come back... (that's happened to me many times, so save before encounter.)
trade from leafgreen
You can't get Zapdos on Pokemon Pearl or Diamond but you can migrate it from Pokemon LeafGreen or Pokemon FireRed.
You have to trade it from Firered/Leafgreen in Pokemon firered/leafgreen you can find zapdos in power plant, but you need surf to get there.
I guess Zapdos
Get the 7th or 8th gym badge, and its in the Power Plant.
You can find Zapdos in Power Plant only once so if you let Zapdos fly away or if you defeat it you can never find it again in LeafGreen.
Use the HM Surf to surf southward from the rock tunnel area soon you will find a building this is the power plant inside you can find zapdos.
In Pokémon LeafGreen Articuno can be found in the Seafoam Islands, Zapdos can be found in the Power Plant and Moltres can be found with One Island's Mt. Ember.
zapdos moltres articuno and mewtwo
Well you can Easily get moltres zapdos and articuno
In Pearl, you can neither find Zapdos, nor Moltres. To get them in Pearl, you'll have to trade or migrate. You can find them in FireRed/LeafGreen, Platinum, HeartGold/SoulSilver and X/Y. If you migrate them from FireRed/LeafGreen, you'll find both of them in the mountain area at Pal Park.
Articuno: Seafoam Islands Zapdos: Power Plant Moltres: Mt. Ember