Seems simple enough, right? Unless you're like me and you're always a little unsure what the best method really is.
There are three main methods. Cold water method, hot water method and the newly discovered (and thoroughly disliked by me) baked method. You can also steam them, but I couldn't find enough information to feel good enough about passing on that information, and since I've never done it...
Obviously the concept is the same, cook the eggs, then cool immediately for easier peeling. I like to prepare an ice water bath to put the eggs in once I pull them out of the water. It's so much easier than running cold water over the hot eggs, cools them more quickly and evenly and since we don't have cold tap water in the summer, it's the only way I can do it.
A few hints:
Fresh eggs are harder to peel. Seriously, they are. I thought this was just an old wives' tale until the last batch that I did, and the three fresh laid eggs in the batch were a beast to peel. Take my word for it, store bought eggs are fine, freshly laid eggs should wait a few days before being hard boiled and peeled.
The ice water bath also makes it immensely easier to peel the eggs. If you fail to cool the eggs well they continue to cook, and they are hard to peel.
Of the three methods described below I always do the hot water method. Why? Because I can multi-task more without worrying about forgetting something. You only have to time the eggs while in the water, instead of watching the water reach a boil, then timing. For busy brains like mine, the hot water method is the way to go, but remember....place the eggs in the hot water GENTLY, or you will have something that looks like egg-drop soup. Only nastier.
I've only tried the baked method once, and I'll never go back. The eggs were harder to peel, and the eggs had little brown marks from the racks which made my kids think they were gross...I know, it is probably just my kids...
COLD WATER METHOD: Place the eggs in a suitable pan with cold water to cover about 1/2 inch over the tops. Place on the burner and cook until the water reaches the boiling point. Turn off the heat and cover. Let stand for 15 minutes and then cool quickly under cold running water.
HOT WATER METHOD: Place enough water in a suitable saucepan to cover the eggs 1/2 inch over their tops. Bring the water to a rolling boil and then add the eggs by gently placing hem in the water with a spoon. Turn the heat back to just below simmering, cover and cook for 20 minutes. Place the eggs under cold running water immediately.
BAKED METHOD: Preheat oven to 325°. Place eggs in oven situated so they won't roll around, without touching other eggs. Bake for 30 minutes. Place immediately under cold water.