Learning to cook eggs is not so simple. I worked as a short-order cook through high school and college. Mostly, what you have to master is saute skills. Pretty much every egg dish can be prepared in a pan. Poached eggs require the most technique, in my opinion. I have seen more people screw those up than any other egg dish. The concept is pretty simple: to essentially steam an egg so what it yields is a soft-boiled egg not in the shell. If you like that sort of thing, you can master eggs. The rest is just frying, flipping and/or scrambling. I was introduced to the three-minute egg traveling in Europe and Asia and it is a really perfect food, too. It is maybe too trying on the patience of a typical American (some folks I know don’t like to eat whole crab for this same reason).
Anyhow, here is a tip: if you like a poached egg, try basting instead. It’s easier, faster, cleaner. What you do is heat up a small non-stick pan (was it the Frugal Gourmet who used to say, “hot pan, cold oil”) on medium-high heat and toss in a bit of oil to coat the bottom (if there is more than the thinnest film of oil, swish out the excess) or, for more flavor, butter. If the pan isn’t hot, the eggs will stick. But, if it is too hot, they will burn. The butter will scorch, too. Now, gently crack in your 2–3 eggs. You might want to turn the heat down some. Let the eggs start to turn white. You can flip them now or leave them sunny side up. Take a lid or plate or what-have-you and drop about a teaspoon of water into the pan and cover for about a minute. You might get splattered if you aren’t careful. Steam should press out from under the lid. This technique works well for melting cheese quickly too, which is even more delicious on poached eggs or hamburgers. If my pan is too hot, I just turn the heat off at this point. Anyhow, it takes some tinkering to make these the way you might want them. The yolk should not be cooked really. Just a few minutes of cooking time. Toss on some coarse salt, some fresh ground pepper and some gorgonzola. Best served with something toasted that can sop up all that yolky protein that is going to smear all over your plate. English muffins or some fluffy fresh biscuits should do nicely. Say, this is making me hungry.
I can describe exactly how I make poached eggs, omelets, etc. if you’re interested.