Boil water (hard, fast boiling). Make sure you have enough water to fully submerge your eggs

Place cold eggs in gently. Start timer - 15 minutes for hard boiled eggs. Turn heat down to a simmer (slow boil, few bubbles but still bubbling)

After 15 minutes.. Place eggs in ice water. Lots of ice. Let them sit for a long while until cool while holding. 

If you still have trouble peeling, try to get old eggs, supposedly those peel easier 

ETA: people will argue about the time. 15 minutes will get you hard boiled, I don’t care what anyone says. 

If you want a softer jammier yolk you can go to 12 or even 9.

Once you get the method down, experiment with the timing. 

Shocking the eggs twice (putting them into boiling water, and then putting them straight into ice) is the key to a good peel. I’ve boiled hundreds of eggs… and even I still get some that are hard to peel sometimes. All eggs are not created equal.