Rather than waiting to post this until I've had time to write up five of them, I'm going to start with just one, and then post more later.
These are one of the things where the recipe is almost trivial, but there is lots of art in getting them just right. (And I inherited lots of pickiness about having my eggs just-right from my mother.) First, mix up the eggs -- they should be scrambled with a whisk or a fork to the point where they are completely homogeneous, with no white streaks. Do not skimp on the scrambling! Add about 1 part in 6 of milk, half-and-half, or cream. Also add a dash or two of freshly-ground pepper, and a dash of dill if desired. Add a tablespoon of fresh-cooked bacon bits, if you've just cooked some. Finally, mix in about 1 part in 4 of grated cheese -- sharp cheddar is best.
Now, for two or three eggs, use a non-stick eight-inch frying pan, on a heat level that's just a little over what it takes to bring a saucepan of water to a rolling boil (one notch past medium on my electric stove). Add a teaspoon of an appropriate fat -- I'd use bacon grease if available, or a curry oil that lilairen made for me, or if neither of those are available, butter. This should be heated to the point where the oil feels distinctly warm to a hand placed about an inch over the pan, or the butter or bacon grease is thoroughly melted and any moisture in it is just beginning to bubble. Ideally, the egg should sizzle lightly when poured in. Before pouring the egg in, though, roll the oil/grease around in the pan to spread it out as much as possible (which, in a non-stick pan, won't be much; it should be hot enough to flow rather than coat), and then pour the egg in right in the middle of where the oil ends up. Some bits of cheese will be left in the bowl; scoop these out into the pan too.
At this point, you have about 30 seconds before things become critical. I use this to turn around and grab the plate that the eggs will end up on. Before putting the eggs in the pan, any side dishes and beverages should be prepared and ready, and you should have a wooden spoon (or plastic equivalent) ready to hand.
So. After about 20-30 seconds, the egg will have formed a bottom layer that is starting to solidify, and is about the consistency of firm jelly. At this point, start stirring, until that bottom layer is completely broken up and evenly distributed in fine curd throughout the egg. You'll need to pay particular attention to the edges, but don't neglect any parts of the middle. Ideally, the temperature of the pan should be such that this layer of beginning-to-solidify egg reforms at about the rate that you can break it up with not-quite-vigorous stirring; keep stirring and breaking it up, stirring as vigorously as needed to do so. Do not stop stirring.
After a minute or two of this, the the egg will fairly suddenly get to a point where there is no uncooked egg left, and it's about half softly solid and half the consistency of thick hollandaise. In the next few dozen seconds (keep stirring!), the egg will go from this state to a state where it's nearly all softly solidified. Somewhere in those seconds -- exactly where depends on taste -- is the magic moment where the eggs are perfectly cooked. At this moment, you immediately dump the egg out of the pan onto the plate, and serve it. Ideally one should start eating it within the minute, but under no circumstances should it be allowed to go cold.