If they're hard to peel they're overcooked. Start by reducing the boil time down to 8-9 minutes. Put the eggs in after the water has started to boil.
If you are having trouble with cracked eggs, put the eggs in cool or room temperature water then add heat. Be sure to adjust your boil time accordingly.
Next, old eggs peel better, much better. In fresh eggs, the albumen sticks to the inner membrane in part due to the acidic environment of the egg. The pH of a freshly laid egg is around 7.6 (average between alkaline-acidic) After the protective coat is washed off the egg (processing), the egg becomes porous and looses carbon dioxide resulting in a more alkaline egg at or around 9.6 pH. Use eggs that are 5-7 days old.
Once the boiling process is complete, remove them from the water. Do not cool them off. Cool them enough to handle but that's it. Warm eggs peel easier. You'll want to start peeling from the narrow or 'pointy' side of the egg. You'll notice on most eggs that there is a small, hollow indentation under the shell, it's an air pocket. This makes a great starting point to peel both shell and membrane alike.
If these steps are followed in their entirity, the shell should fall right off. Good luck!