Frustrated with the many different directions, tools, utensils, advice, etc on how to hard-boil eggs, I finally went to my local library and picked up a cookbook (Maran Illustrated Kitchen Techniques) describing, in detail, the steps to make consistently good hard-cooked eggs. It hasn't failed me yet -- though the last time we did this, I was a little too vigorous in shaking my eggs. We ended up with bitty bits of eggshell everywhere!
Place the eggs in a saucepan, arranging them in a single layer. Fill the saucepan with cold water until the water level is 1" above the eggs. Add salt to the water. Bring the water to a boil. Boil for 30 seconds, place lid on saucepan, and remove from heat.
Let eggs sit in the hot water for 15 minutes. Do not drain, but, rather, run cold tap water into saucepan for 2 minutes. Let eggs sit in the cold water for 3 minutes. Drain.
Cover. Holding lid firmly in place, shake the saucepan for 10 seconds to crack the shells of the eggs inside. Starting at the largest end of the egg, begin to peel off the shell. If you have difficulty removing the shell, place the egg under running cold water as you peel the egg.