Break the eggs into a bowl, add the salt& pepper and milk/cream if using. Mix well with a fork - don't beat or whisk it!
In the meantime heat a smallish frying pan on the hob. When it's hot, add the butter and let a melt & bubble but not burn. Pour in the eggs, then tilt the pan around to allow the eggs to spread out evenly.
When the omelette is almost cooked through (its surface is still slightly wet), using a spatula, fold it in half.
Cook for a few more seconds, perhaps flip it over once.
When it turns golden, slide the omelette onto a plate.
Version 2:
You can make the omelette more fluffy by tilting the pan, then, with a silicon spatula, drawing the edges of the omelette into the centre. Tip the pan again the other side and let the egg spread around whilst pulling in the edges of the cooked egg. Keep doing this until the eggs are cooked through. Then flip, fold and slid on to a plate.