For fifty years or so I always made omelets the same way: whisk a couple of eggs in a bowl with a fork; salt them a very little bit; melt a piece of butter the size of half a walnut in a pan; heat until nearly brown; throw in the eggs; quickly rotate the pan to move the eggs around; flip; invert them onto the plate.
Of course the devil's in the details: what pan, how hot, how shaken, etc., etc.
And two or three years ago a movie changed my method. In the closing sequence of Big Night a cook makes an omelet in an Italian restaurant. The scene plays in real time: he mixes the eggs, warms the pan, cooks the omelet. The soundtrack is nothing but the sounds of the preparation: no music, no dialogue.
And instead of butter he uses olive oil.
Cheap pinot grigio.