Purchasing Nests
In order to get or hatch eggs, you have to have an adequate amount of nests. Nests are purchased with the points earned by the worker P3s. In "Neopets" your P3s -- also referred to petspetspets -- are categorized as either nesters, soldiers or workers. The workers earn the points that allow you to buy nests, and the nests are essential for being able to hatch the eggs that you eventually hoard.
Worker Population
After a suitable amount of nests are purchased, let the worker population die. The worker pets are responsible for helping the habitarium grow and develop, but are not essential for collecting or hatching eggs. Therefore, you can let these pets go and be replaced by nesters. You can also replace some of the soldiers, too, but leave a few to help defend the habitarium.
Increasing The Nesters
As the worker population becomes extinct in your habitarium, and is replaced by nesters, your nester numbers increase. This benefits your cause for getting habitarium eggs, because the more nesters you have the more eggs you can get. This becomes a cycle of the nesters hatching the eggs, which spawn new P3s, which triggers the need for more eggs that the nesters can continue hatching.
Effort
It takes effort on the player's part to keep up the egg cycle of nesting, hatching and harvesting. The player must actively participate in the process so that the hatched eggs are harvested timely before they have a chance to rot and die. This means having to check on the eggs in the nest every hour or so to make sure you haven't missed out on the time restrictions. You can tell that an egg is ready to hatch and be harvested when it starts bouncing up and down on the screen.