I place the eggs in the pan they were cooked in and add cold water.
I then crack the eggs under water (this seems to help loosen the membrane under the shell).
Start peeling at the larger end, where the air pocket
is, and remove the shell under running water to make the shelling easier. You must get a hold of the membrane under the shell when you remove the shell. Very fresh eggs are harder to peel. The fresher the eggs, the more the shell membranes cling tenaciously to the shells.