This page explains how to get eggs in Pokémon GO and how to make them hatch.
How to Get Eggs
Eggs can be randomly found at PokéStops. They seem to be less likely to appear than Pokéballs.
Viewing Your Eggs
To see the eggs that you have, tap the Pokéball icon in the main screen, then tap the Pokémon button. Then tap the "Eggs" tab in the upper corner. This will show you all the eggs that you have.
Incubating Your Eggs
To make the egg hatch, you first have to put it into an incubator. Tap the egg, then tap Start Incubation to choose an incubator from your inventory.
You always have one infinite-use Egg Incubator. You can only use it on one egg at a time, so if you want to incubate multiple eggs a time, you will need to purchase additional incubators from the shop. However, the incubators that you can purchase from the shop can only be used a limited number of times. After they are used up, you will have to buy more from the shop.
Hatching Your Eggs
Each egg has a distance below it. This is the distance that you will have to go to make the egg hatch. However, you have to have Pokémon GO open on your device to increase the distance. Also, the distance will not increase if you are moving too quickly, i.e. if you are in a car, airplane, or other fast vehicle.
Eggs and Distances
The rarer the pokémon in the egg, the farther you have to go to hatch the egg. Eggs that contain more common pokémon will require 2 km of distance, while eggs that contain the rarest pokémon will require 10 km of distance.