The best way is start with your eggs in cold water on high heat, when the water comes to a full boil cover and remove them from the heat, let them stand for 20 minutes and then run cold water until nice and chilled. Boiling the whole way thru the cooking process causes a green ring around the yolk.
don't boil them completely submerged in water, at least the water level should reach half the eggs length. it can be cooked in 15-20 minutes, fire should be moderate because high fire can make the water boil briskly, this may crack the egg. start counting when the water boils.:-)
actually, the altitude can make a difference on how long it takes. When I was just a few feet above sea level I swear it took several minutes less to cook an egg than it does not that I am 4000 ft above sea level