Put the eggs in a pan of COLD water, making sure the water is at least a half inch over the top of the eggs.
Put the pot, without the lid on HIGH heat.
When it comes to a boil, REMOVE the pot from the heat and put on the lid.
Take the pot OFF the heat and leave it with the lid on for 20-25 minutes.
Dump out the hot water and run cold water over the eggs. Crack on the counter and peel right away. (You need to peel them right away so you don't get that greenish tinge to the yolk.)
Note: Fresh eggs are harder to peel than eggs that you get from the store. I always buy store eggs rather than farm eggs when I have to make a big batch of devilled eggs.
You can use this method for soft boiled eggs too - just leave them covered for 3-5 minutes.