How to Obtain
Eggs can be obtained in a variety of ways. The main way to get eggs is from the Nursery, where you can earn Care Points and buy them. Common eggs are purchased directly, while buying an uncommon or rare one gives you a random egg of that rarity.
While buying eggs is the usual way of obtaining them, some tasks and events also offer them as rewards.
How to Use
In addition to buying eggs at the nursery, you can also use them there. If you've purchased a nest, just place an egg in there. You, and anyone else in the group, can now pat it to raise its percentage and earn Care Points. Once it's been pat enough to reach 100%, you'll be able to hatch it into a chockin. You'll also receive an Eggshell for each egg you hatch, no matter what's inside it. How much closer it gets to hatching from each pat varies based on nest level, but other factors can influence it too.
Eggs come in four different rarities that vary in price and content. The rarer eggs are more expensive, but more valuable Chockins can hatch from them.