Of all the hundreds of egg dishes in Mexico, this is the only one that gets called "Mexican-style eggs".
It's a simple dish of scrambled eggs with chopped tomato, chopped green chiles, and chopped white onion.
The colours are important because they represent the Mexican flag. So you can't use red chiles or dried chiles.
Basically, chop the chiles, onions, and tomatoes, and fry for a minute (you still want a bite on the onions).
I fried mine in home-rendered bacon fat.
Then season your eggs and scramble them with the chopped ingredients until just done.
I served mine on a warm tortilla with some Gran Luchito.
I would happily eat this for breakfast every day of my life.