It helps to have fresh eggs  . . . I use a non-stick pan on med heat (300°F) and add some butter. Crack the egg in. I have to flip them at that heat so I wait till the egg is about ¾ cooked and flip to finish the whites/yoke. I do not like anything but over easy eggs . . . can't stand hard yokes or over cooked whites.

I've never tryed the adding water and covering the pan .  .. I'd have to use a much smaller pan I think . . . .