I used to hang out at my friend's house a lot. My friend's mom would always be making tamago and dumping it into our sweet bean summer soup. I decided to learn from her one day since I was kind of bored from hanging out at home. =]
Whisk eggs in a medium sized bowl until smooth. Then stir in Sugar and soy sauce until it becomes throughly mixed in. No lumps. Heat a frying pan at medium heat. Melt about ½ tbsp butter in the pan, spreading it so the bottom of the pan is completely covered. Pour the egg mix into the pan. When the egg looks opaque and you can get a spatula under it without tearing the omelet, flip the omelet. When the omelet is coked through (you can lift the omelet with the spatula to check underneath), remove the omelet from the pan. Slice into thin strips. The width of these strips depends on what you are using the tamago for.