An easier omlet is made by using a square, non-stick grill pan. Lightly butter or grease the pan, then wipe with a paper towel. Break 2 large eggs into a bowl with a splash of milk. Season with salt and pepper and whisk until the yolk, whites, and milk are evenly combined. Pour into the center of the pan, and swirl to coat the entire pan, right to the sides. Cook over medium heat until the top is set. This works because the egg is thin. Sprinkle on toppings, cheese first, again, all over the top. With a long, plastic spatula, fold one side 2/3's accross. Fold the other side the same way. Slide onto your plate.
This is an American style omelet. You can fill it with anything you want.
Classically, the round omlet is made in a saucier, typically, non-stick. Again, lightly lubricate the surface. Mix the egg in the same say, and pour into the pan. Swirl to coate teh entire pan bottom, and a touch up the sides. When the egg starts to cook, push it from the sides to the center, one time. This causes the uncooked egg to drain off the top, and onto the hot pan. Cover and let cook for about a minute. Remove the cover and the top should be set. Add toppings to one side. Slide omelet from the pan, onto the plate, using the pan to fold it in half. Place the pan lid over the plate and let sit for a minutes to let the residual heat melt the cheese.
The key to good omelets is to use a very slippery pan, and to get the top set without having to flip the omelet, and not to overcook the bottom. I've even been known to place the pan under the broiler for a moment, to set the top, if things weren't going well on the stove-top; but that's a rare thing, maybe did it once.
Seeeeeeya; Chief Longwind of the North