Allow hard-boiled eggs to cool before removing shells
If you hard-boil eggs in water and then try to peel the shells off right away, your efforts will be futile. Chunks of the egg will come off, and your fingers will be unable to reach all of the pieces of eggshell that you require. Allowing your hard-boiled eggs to cool completely is the first step toward easy peeling.
When your eggs are done, place them directly in an ice bath to stop them from cooking any further and to speed up the cooling process. Before peeling or putting the eggs in the refrigerator, place them in an ice water bath for about 15 minutes. Start peeling your hard-boiled eggs at the top of the egg, where the air pocket is. It's also worth noting that older eggs are typically easier to peel because the yolk and whites are firmer, so save those farm-fresh eggs for scrambles or frying.