To peel the egg, lightly tap the egg on a hard surface to crack the shell. Once the shell is cracked all the way around, it should easily peel away from the egg. Once the shell is removed, briefly rinse the egg under water to remove any small bits of shell that may still be attached.
Any eggs that you do not plan to eat immediately should be left unpeeled and refrigerated. Unpeeled hard-boiled eggs will stay good in the refrigerator for up to a week.