i've worked at waffle house for over five years and one sure way to get any cook to argue is to ask, "what's the right way to cook an "up" egg?... I'm willing to learn things from everyone no matter what their experience level, but for me there is one, "true" way to go about this method. I go by food network standards,
which pretty much means low and slow. I cook on a flat top, but when I have time I simply crack two eggs into a well oiled seasoned pan, place it on the low heat of the grill, and watch as the rest of my order cooks from beginning to end, so will my egg whites evetually. if it looks like by the time my egg whites are going to be done my yolk could be overdone, first and foremost this means the grill is a little too hot, but i simply use a spoon and put it in the uncooked white and press it to the bottom, "scooting it" a little, breaking open the cooked part underneath the gelatenous undercooked section, and now allowing the more gelatenous uncooked part of the white to cook along the newly created space at the bottom of the pan.
Given all the debate on this topic, nothing can say it better than a pictorial and step by step on how beautiful, and perfect sunny side up eggs can really be. The yolk should be runny, but thicker than over medium yolks, there should be no part of it that is overcooked like a well done yolk, and yet the wites, soft, but completely white, no undone runny, raw egg. No browning whatsoever need be on ANY egg that I EVER cook, whether it be over well, an omelet, or anything. I was trained by a great breakfast cook who would throw away eggs if i made them perfectly...(minus 1 freckle of brown). I can't tell you how many times I see cooks cooking "up eggs" at too high of a temp, overcooking the bottoms, then scraping off the uncooked off the top. GROSS.
And as far as covering your eggs: I work at a restaurant; I am a short order cook; I do what I have to when shit gets crazy, and yes I have covered them for the last few seconds of cooking time, but that would basically fall in line with basting, and someone else mentioned it toughens the egg, it may look right (except it's easy to do it for too long then not only is it technically basted, it LOOKS basted, with a white film over your once beautiful yellow yolks) but that's not how you make sunny side up eggs! If you cover them, that's not making them sunny side up, period. Just like you can make pulled pork in a crock pot and throw barbeque sauce on it it doesn't mean it's barbeque. Sorry, it may still taste good, but it's not.
HERE'S THE BOTTOM LINE: I feel that the best way to simply put this is 1.) oil pan 2.) add one or two eggs 3.) cook low and slow. They should come out perfect if you have any patience.