Using the Masterball. But, I wouldn't recommend that. There are other Pokémon that you would be better off using the Masterball on.
The usual stragety is to slowly knock away its HP down to the red zone, and then give it a status problem. Most common is Sleep, because that way Zapdos won't be able to attack until it wakes up, but Paralysis works just as well. After that, just keep throwing Ultraballs (for a better catch rate) and just hope for the best.
Any Pokemon it doesn't matter but no matter what the easiest way to catch them is by using the master ball now i know you only get one of it but that's the easiest way. Besides that the best strategy to catch any Pokemon is to weaken them as much as possible, inflict a status problem on them all though burn and poison are not the best options but you can use them and then use a pokeball that is best to catch the Pokemon let me explain more: If its a weaker Pokemon you can use a great ball or ultra ball to make sure you catch it also using a nest ball would be good as well, If you caught the Pokemon before and just want another use a repeat ball, If a lot of turns have been made use a timer ball, If its a water or bug type Pokemon use a net ball, Stronger Pokemon must be caught with an upgrading poke ball like the great ball or ultra ball.
Throw a master ball at it.
You can capture Moltres at Mt. Ember Peak and Zapdos in the Power Plant in FireRed.
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There is only one Zapdos, Articuno, and Moltres in Fire Red.
You can capture Zapdos from the Powerplant. You will need Surf, And you need to go to Route 9 from Cerulean City, All the way to the PokeCenter. Above the Center, there is some Water where you can Surf down to the Powerplant. Just sole the Labyrinth, and get Zapdos! Remember to save in front of it! ^^
Articuno, Moltres, Zapdos, Mewtwo, Suicune, Raikou, and Entei. C Dawg
You can capture Moltres at Mt. Ember Peak and Zapdos in the Power Plant in FireRed.
You can capture Mewtwo in Cerulean Cave B1, Zapdos in the Power Plant, Articuno in Seafoam Islands B4, and Moltres at Mt. Ember Peak in FireRed.
you can't capture it in soulsilver but you can trade it from pearl,diamond,or platinum
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You can't get Zapdos on Pokemon Pearl or Diamond but you can migrate it from Pokemon LeafGreen or Pokemon FireRed.
In the power plant(Zapdos is hard to find but its is there).
No you must migrate zapdos from leafgreen or firered then capture it in pal park (NOTE:You must beat the Pokemon league before you can get acces to pal park.)
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.
yes at the place where you get zapdos
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You get him where zapdos is (power plant)
There is only one Zapdos, Articuno, and Moltres in Fire Red.