It’s important to boil the water with the eggs already in the pot, because plopping raw eggs into roiling waters will almost always result in broken shells.
Lastly, this is one of the only times you want to use older eggs. Fresh eggs have a tighter grip on their shells and will make peeling a pain. The best test is to submerge them in water. If they lay flat, they’re fresh. If they stand on end, they’re perfect for boiling.