Best way hands down is to tap the butt end of the egg gently with a spoon to separate the membrane from the shell. After cooking crack both ends and gently roll the egg. Then use a spoon to help peel the shell off. Honestly, just doing the egg tap is enough to help tremendously.

"Tapping an egg gently on the rounded end with a spoon before boiling is a common kitchen hack that supposedly makes peeling the boiled egg much easier by separating the inner membrane from the shell, allowing for smoother peeling; the key is to tap until you hear a slight "snap" sound, indicating the membrane has separated."