If possible, use organic eggs or ones bought from a farmer who lets his chickens roam and eat grass, insects, larvae, etc. (They'll have more flavor and nutrition.) Commercial eggs from factory farms can spell danger.
I’ve heard many different ways of making hard-boiled eggs, but this is how I do it:
Put eggs in a pot. Add enough cold water to pot to cover eggs by about an inch. Turn on heat, bring water to a boil. When water starts to boil, lower heat, bringing water down to a simmer. Continue to cook eggs for nine minutes. Remove eggs and immediately place in a bowl of very cold water (the colder the better), which will stop the cooking process. Peel and eat immediately or store in refrigerator unpeeled for about five or six days.