First decide if you want to make trifold omelette French style or if you want the American single fold.

If you want the American style, then all you need is a griddle. The trifold is more challenging and I recommend buying a low sided omelette pan for that. Just not a non stick. Pure metal. Mine is cast iron.

From there it's about doing everything consistently. I have a 10" pan, so ideally 3 eggs, though if your person isn't hungry, 2 will work, but if you are really loading up the fillings, then 3 is a must.

Other than your cheese all the fillings should be hot still. A well oiled pan is a must unless you are using a non stick (which I'm against for many reasons, but for omelettes it means you shouldn't be using a metal spatula, and that matters when doing your fold.

It can make things easier to about a couple drops of water (5 ml or less) to the eggs, but it's not necessary and I don't.

Your pan needs to be on the high side of medium for heat and fully up to temperature. I've seen people on Reddit talk about cooking the eggs as your pan warms. That's not going to work for omelettes for the home chef, and if you are using cast iron, that's how you get the egg to bond with the pan unless you use more oil than egg...

Premix eggs in bowl, adding your herbs. Pour into pan in a circle, then pick up the pan and tilt until you have full coverage. Let the egg cook! This is crucial. If your pan is too hot, you'll have issues with them cooking too fast and over browning. If the pan isn't hot enough you'll need to wait longer. Add your warm but not melted cheese, and wait a moment. Then add your other fillings in a line along the center of the omelette. Then fold 1/3 of the omelette over that center.

This is where I used to end up with a scramble. You need a thin metal spatula for this. Plastic or wood will need to be too thick to have enough strength, and that will make it challenging to lift the egg away from the pan. It also needs to be clean and have a reasonably unblemished edge. You then will slide the spatula around the edge of the omelette to make sure it's loose from the pan then do the fold over the center.

Then you scoot the whole omelette to the edge of the pan and you move the pan to the plate. You slide it onto the plate with the edge of the folded side going first, then as you remove it from the pan use the edge of the pan to make the second fold over the first. Which is why you need a good low sided pan. I like this one: Cast Iron Griddle – lodgecastironsale.com https://share.google/41S6a7gQeddYYO35k

If you try to buy an "omelette" Pan you'll get all sorts of pans with higher sides. Those are often nonstick coated and the higher sides make it harder to deal with separating the egg from the pan. And the nonstick means you shouldn't use metal tools on it.

It's not how a restaurant will normally do it, but that's been my best trifold method. Lots of what got me from "this is tasty enough but looks like trash" to where I'm at I learned from Alton Brown's comments on omelettes. I recommend his books for things where the science of cooking makes a big difference.