Here's how I do it. I put enough cold water in the pan to cover the eggs. I'm with lvpets2002 - just a bit of vinegar so they cleanly peel. I hate trying to peel an egg and having it look like a golf ball when I'm through. Put in the eggs (I use a serving spoon), cover the pan, and turn on the burner. When the water boils, shut off the burner and set a timer for 20 minutes. When the timer beeps, I like to take the eggs out of the hot water - I usually pop them in a bowl of ice water if I need them right away, or just cold water from the tap if not. I water my plants with the egg water when it's cool - supposedly the egg water is good for plants. My brother likes eggs a little softer so he takes them out at 15 minutes instead of 20.

And, on the subject of deviled eggs - I like the filling with mayonnaise, yellow or brown mustard, a little paprika (black pepper will do in a pinch) and a spoonful of sour cream or plain yogurt to make it smooth.