You can find elaborate omelet instructions in any reputable cookbook, and you can buy special pans. My advice is to relax – you’re just cooking eggs! I do think that a regular little non-stick skillet makes it easier, but any omelet-sized skillet with sloped sides will do.
1/4 cup grated cheese
1 tsp. butter
Put eggs in a bowl and beat lightly. Add 1 tsp. water. Heat skillet and add 1 tsp. butter. When butter is melted and foamy, pour in eggs. Cook over medium heat. As eggs set, lift edges of omelet and let uncooked egg run underneath. When omelet is set, reduce heat to low and put cheese on top. Cook 1-2 minutes until cheese starts to melt. Loosen edges of omelet and slide on to plate, folding omelet in half as you do so.