What I do is I put them in cold water and bring the pot gently to a boil. Sometime I put vinegar and I always put salt because vinegar helps by keeping the white from spreading if any eggs cracked and salt keeps them from cracking when you boil them and makes the eggs easier to peel, afterwards.
Once the water boiled (or a little after, it's still ok, but don't let them in too long), I turn off the heat and let them gently cool down for about 12minutes. I set an alarm for that :) Then I put the eggs in cold water to stop the cooking. Normally I would change the water once or twice when it's too warm but I don't usually have so much time any more. Your eggs are now perfect for painting, dipping them in dye and so on.
In Romania, for Easter, we have a tradition of cracking eggs, you basically smack your opponent's painted egg with yours, but if you just want to enjoy your perfect hard boiled egg, you can gently crack it once by tapping it against the table then, gently, roll the egg on a hard surface, applying a little force. The crust will crack in more pieces and it will be easier to open. Also, water helps with peeling. Don't trust me? Try it! And, have a great, sunny Easter!