Fill a bowl with ice and water. When you are done cooking the eggs, transfer them directly to the ice water. Let cool for 10 - 15 minutes.
When peel the egg, don't use your fingernail or pinch the shell. Instead, push the shell off. It will glide away from the egg. The whole egg can be peeled and all you will have is one or two pieces of shell. Very simple, fast, and the egg looks pristine because you didn't damage it getting the shell off.
Paradise Lost - Tom Brady