Picking your pan. You can knock yourself out finding, seasoning, and caring for a special heavy-gauge steel pan specifically made for omelets, but I've been happy and successful making omelets in my good-quality nonstick aluminum pan. Choose a pan with a heavy base and sloping sides, six to eight inches across the top, depending on how many eggs you're using.
A mix of butter and oil gives you flavor and a high smoking point. You can use butter alone, but you have to be careful not to let it burn. I like to heat a teaspoon of vegetable oil over high heat and then add about a teaspoon of butter. Another option is to use clarified butter, made by melting unsalted butter and pouring off the liquid, leaving the milk solids behind. Clarified butter gives you the flavor of butter with a higher smoking point.
Add the eggs when the fat is hot and emits a slightly nutty aroma. If you're not sure if the fat is hot enough, add a drop of egg: it should hiss when it hits the pan.
Vigorous stirring and shaking cooks the omelet evenly. A fork, held flat so as not to scratch the pan's surface, works better than a whisk to create small curds for a creamy, not clumpy omelet. Keep the eggs in constant motion, shaking the pan and stirring with the fork, until the eggs begin to set, about 20 or 30 seconds, depending on how many eggs you're cooking and the intensity of the heat.
Stop stirring while the center of the omelet is still moist; this allows the omelet to set neatly. If the eggs aren't evenly distributed in the pan at this stage, spread them out with the back of the fork, and then use the fork to neaten and loosen the omelet's edges.
The "roll" is actually more of a fold. You want to fold the near edge away from you toward the center of the omelet, and then fold the far edge toward you to the center.
The first fold is best accomplished by lifting the edge with the fork and folding it over. The second is achieved by manipulating the pan, as shown in the photos.
Once you've slid the finished omelet onto your plate, you can neaten its shape with the fork or a spatula.
I usually let the omelet set this way for another 30 seconds or so. This lets the outside of the omelet brown slightly yet keeps the inside moist. If you find you like a slightly more cooked omelet or one that's a little looser, adjust the time accordingly.