I know it's not brain surgery but since I don't hard boil eggs very often, I have to relearn the method a couple of times a year.
Underboiling results in a runny middle (or, erm, "soft" boiled egg), while overboiling turns the yolks a greyish green. Using the method below, you'll get a nicely cooked hard boiled egg, perfect for dying, turning into devilled eggs or simply eating with a dusting of salt and pepper.
Perfect Hard Boiled Eggs (method source)
12 large eggs, room temperature
Place eggs in a large saucepan and cover with cool water by 1 inch. Slowly bring water to a boil over medium heat; when the water has reached a boil, cover and remove from heat. Let sit 12 minutes.
Transfer eggs to a colander using a slotted spoon and place under cool running water to stop the cooking. Eggs can be peeled and served immediately. Remaining eggs, with shells on, may be refrigerated in an airtight container for up to 3 days.