OK... Here's my sure-fire, never-fail (well almost) method of hard cooking fresh eggs.
Get a steamer basket like the kind you would steam veggies in (I have a metal one) and put about 1 inch of water at the bottom of a pot. Place the steamer in the pot and the eggs in the steamer. Cover the pot and heat until the water boils. Turn the heat off and let the eggs sit (steaming) for about 25 minutes. Take the steamer with the eggs in it and submerge in cold water. Peel the eggs when they cool and you should have shells that come right off.
Get a steamer basket like the kind you would steam veggies in (I have a metal one) and put about 1 inch of water at the bottom of a pot. Place the steamer in the pot and the eggs in the steamer. Cover the pot and heat until the water boils. Turn the heat off and let the eggs sit (steaming) for about 25 minutes. Take the steamer with the eggs in it and submerge in cold water. Peel the eggs when they cool and you should have shells that come right off.