There really is no best way, I've tried putting them in when the water is cold and heating, when the water is warm, adding vinegar, baking soda, salt etc.
Using older eggs for better peeling, room temperature or even warm eggs helps them cook evenly, gently boil or not even boil (eggs actually don't need boiled, it's just quicker.) Don't 'shock' in cold/ice water, makes peeling worse. Steaming them actually works better. Those little vinyl egg timer things shaped like eggs help.