The easiest way to peel hard-boiled eggs is to place them in ice water immediately after cooking. After shocking the eggs in ice water, use the back of a spoon to crack the shell at the broad end and gently peel the rest of the shell from the egg.
First, place a substantial amount of ice into a bowl and fill the bowl with cool water. Place a strainer in the bowl to create a separate area for the eggs to rest and make it easier to remove the eggs after they are fully shocked. After boiling the eggs for the desired amount of time, remove the eggs from the pot and place them directly into the strainer in the bowl of ice water. Allow the eggs to rest until they are fully cooled off and no longer feel warm to the touch.
After the eggs have fully cooled off, take an egg out and locate the broad end, opposite of the narrow end. Using a hard object such as the back of a metal spoon, tap the broad end to crack the shell and expose the air pocket. Using the exposed air pocket as a starting point, gently peel the remainder of the shell off by using a thumb to separate the membrane from the egg white until the shell is completely removed.