To peel hard-boiled eggs, place them in ice water first, as this keeps the egg membrane from sticking to the egg white. Another tip is to start peeling the egg from the wide edge. This is where the air pocket is, so it is easier to peel.
Hit the egg against the counter, and roll it on the counter to let the shell break around the egg. This is a standard way of peeling an egg. Another option is to put the egg in a glass, add a little water and start shaking the glass. The shell begins to crack as the egg is shaken in the glass. Putting a little vinegar in the glass with the water can also help peel the egg faster and easier.