To make hard- or medium-boiled eggs easier to shell put them into cold water as soon as they are cooked (as you do anyway for hard-boiled eggs) and leave until cold. Tap the shells all over on a hard surface before peeling.
Shelling the eggs under cold running water also helps remove the membrane between the shell and the egg.
Keep the shelled eggs in a bowl of cold water or in a polythene food bag in the refrigerator until needed, as this prevents the whites going tough. Pat dry with kitchen paper before using.