Since Pidgey need only 12 Pidgey Candies, it is easier to evolve than other Pokemon. Additionally, Pidgey is very common and can be found practically everywhere, making it very easy to get Pidgey candies.
3. Good combination with Lucky Egg
Unlike other XP sources, you can evolve Pokemon whenever you want, and gain XP based on the number of Pokemon you Evolve. By stocking up on Pidgeys and Pidgey Candies, you can gain 1000XP for each pidgey you evolve within 30 minutes (The time limit of Lucky Egg).
1. Capturing Pidgey
Pidgey is extremely common. You can capture a bunch of Pidgeys while looking for PokeStops or doing other things.
2. Transferring Pidgey
Transfer Pidgeys to Professor Willow to get the more Pidgey Candies. Pidgey needs 12 Pidgey Candies to evolve, so you will need to stock up on both the Pokemon and the appropriate candy. Make sure for every 1 Pidgey you want to evolve you have 12 Pidgey Candies.
3. Using Lucky Egg
After finishing steps 1 & 2, you would want to use a Lucky Egg to double your XP gain for next 30 minutes. If you want, you can evolve Pokemon other than Pidgeys while Lucky Egg is active.
4. Transferring Pidgeotto
After step 3, you will be left with a bunch of Pidgeottos that you don't need. Transfer them to Professor Willow to get more Candies, then go back to step 1.
Why is 'Pidgey Marathon' the Best?
900XP gained by a Pidgey evolution
Pidgey need 12 Candy to evolve into Pidgeotto. To get 12 Candy, 4 Pidgey have to be captured. You can gain 400XP by capturing 4 Pidgey and 500XP by one Pidgey evolution, therefore 900 in total.
While Lucky Egg is active, your XP gain is doubled. You can earn 1,000 XP for every Pokemon you evolve.
500XP × 2 = 1,000XP!!
PokeLevel is very nice tool to optimize the effect of Lucky Egg. Tap the link below to see the details of the tool and how to use it.