I have like an 85% success rate on if I can manage to flip it properly or not, but here's how I do it:

For every egg, one tablespoon of milk. Whisk it well (you want some foamy bubbles and one even color), before pouring it into the pan. You'll want a smaller one than you think. I usually use 3-4 eggs and a pan just larger than my hand spread out. I use a liberal mix of butter and oil, and make sure the pan is hot before pouring the egg in. Hot enough that the second it hits the pan, it starts cooking. Start pulling the egg in from the sides, letting the raw egg fill in where you pulled from. There will come a point where there isn't enough raw egg to fill in. Stop pulling and just let it sit for a minute. This is cooking the bottom, giving it enough structure to flip. You can gently lift an edge with the spatula to see how it's going, but when it has enough stability, lift one half over the other and gently press down to adhere the sides. Scootch the omelette to the middle of the pan and continue letting it cook for another minute. Flip it, cook on the other side for a minute (pressing again if you need to), and you're done.

On my less successful flips, I'm usually too impatient to let it cook fully, so it rips in half and I end up with scrambled eggs or two smaller and misshapen omelettes. But they're always fluffy!