I've been publishing articles here at Seasoned Cooking for fourteen years now and every year, like clockwork, someone asks me about how to boil eggs so that the yolks aren't too hard or discolored. It's not what I've considered a best-kept secret or anything, but the rarity of a properly hard-boiled egg was brought home to me once when my sister called me in the evening and had me walk her through the process and, a day later, called to tell me that people at work had marveled at how perfect the inside of her hard-boiled egg looked!
Begin with a clean pot and clean eggs. Arrange them in a single layer on the bottom of the pot and cover them entirely with cold water. Put the pot on the stove over high heat and place a lid over the pot. Bring the water to a boil and turn off the stove. Allow the pot to sit on the stove, covered, for 15 minutes. Then drain the water off the eggs and run very cold water over them to stop the cooking process. I like to dry them and then put them into an egg carton -- you might want to label it so that you don't confuse your hard-boiled eggs with your uncooked ones!
There you have it. No big secrets, but you will get perfect hard-boiled eggs every time. Enjoy and have a very Happy Easter.