Put cold eggs in cold water. Bring the water up to a boil. As soon as the water boils, turn the pot off. Leave the lid on the pot, and let the eggs sit for 10 minutes. Run them under cold water until the eggs have cooled back down and they're ready to peel and enjoy.
If you're having a tough time getting the peel to release from the egg, try peeling them under cool running water. It really helps the skin come away from the egg.