In culinary school, I had to learn to make a proper omelet and be graded on it, but I didn't LIKE it! Let's face it- flipping an omelet can be hard. I know- some people can make the perfect omelet every time- sigh...I passed that phase of my course, and really never did it again. After that, I cheated! Here's how I do it now.
For a two egg omelet, first begin with a non-stick skillet. It absolutely doesn't have to be expensive. I have used the best cookware over the years, and finally discovered that a non-stick skillet that costs seventy dollars and has a designer name on it really lasts no longer than one that you buy for six bucks (that is, the non-stick part.) That part all wears off eventually. So, now, I go to the Dollar store and get one for six bucks. The non stick part lasts just as well and the pan does the job I want.
So, for a two egg omelet, first liberally coat your skillet with olive or coconut oil. Put it on the burner over medium heat and let it heat while you are getting your eggs ready. Break your eggs into a bowl that is deep enough for ferocious whisking, add 1 teaspoon olive oil and really whisk till the eggs are a lighter color and very frothy. Pour the eggs into the heated skillet and let them sit and slowly cook. As the bottom just begins to set, take your spatula and go around the edges, releasing some of the egg beyond the borders of the omelet. Let it cook a little while longer, and then flip. To flip, take a really wide spatula and put it under one edge and gently turn that side to the middle of the omelet. Then, go to the opposite side and repeat, but this time, flip that side onto the omelet side you have already cooked. Let it slowly cook till set and scoop it out onto a plate with that really wide spatula.
I buy a non-stick appropriate spatula that is about five or six inches wide. This helps control the omelet when flipping, and also makes it easy to get the omelet out of the pan without breaking.
Note: if you are using veggies for fillers, you must cook them prior to putting them in the center of the omelet. If you use veggies or cheese, place them in a line along the center of the omelet before beginning the flipping. I usually saute my veggies in the same skillet and when they are done, scoop them into a bowl, add a little more oil, and then begin the omelet.
Also, eggs are much more tasty if they are cooked slowly. Don't use high heat.
This method works every time, and it doesn't make me irritable by breaking before I get it out to the plate. Give it a try- it really works!.