Add baking soda to a pot of cold water. Make sure the eggs are covered by 2 inches of water. When the water reaches a rolling boil, let them slow boil 12 minutes; remove from heat. Stop the cooking process by adding ice to to the water. Slightly shortening the recommended length of boiling time leaves the eggs done, but without drying the yolks. As soon as the eggs are cool enough to handle, peel them.
Tap the end of the egg, remove shell. Tap the other end of the egg and remove shell large enough for the egg to exit. Then you can literally blow the egg out of its shell into your hand. For sanitary reasons, I recommend just removing the shell with your fingers.
It has been said that the key to peeling them easily is not to let the egg cool all the way, but this video says it's because of the PH level of the water from the baking soda.