"Making omelets is like riding a bicycle," writes Wayne Gisslen in Professional Cooking. The process can seem awkward and difficult at first, but it becomes intuitive and easy once you get the hang of it.
The French stir the eggs carefully as they set, generally limit themselves to cheese by way of filling, and fold the omelets into thirds. We Americans lift the edges of the eggs as they cook and let the raw parts flow underneath (ducking the danger of ending up with a scramble), and we tend to load up the finished product with all sorts of fillings, making one-third folds a pipe dream. A half-fold handles the layers of tomatoes, olives, ham, greens, and the like.
Here, we go with the American cooking method but give you the choice of folding the omelet into thirds or in half, depending on what your fillings allow. The trick is to cook the eggs over fairly high heat and keep lifting the edges as the bottom sets, then to serve the omelet immediately.