When the timer goes off, carefully remove the eggs from the pot with a spoon and place into a bowl full of ice and water. The ice bath will cool the eggs quickly and stop the cooking process. The ice water will also cause the egg to contract and pull away from the shell which will make it easier to peel. Let the eggs sit in the ice bath for at least 5 minutes.
If you live in a climate where tap water runs very cold, you can run cold water over the eggs for five minutes rather than preparing an ice bath.