Tap the cooked egg all over it, peel off a tiny bit of the shell and skin, then gently insert the tip of a table tea spoon under the shell and skin, it will slide under the skin and peel the egg and will be ready to dunk into water and make into deviled eggs.
I use salt, pepper, barely enough red vinegar to moisten the whole chopped bunch of eggs, sweet pickle relish, finely chopped onions, a little German mustard, mayonnaise, touch of mustard, anything that looks good goes into this. And at parties none of mine are ever left to bring home. The egg mixture left over makes delicious sandwiches or lovely piled on small crackers. Added to it a slice of sweet pickle, a tiny slice of strong cheese, really makes a nice snack.