I got this recipe from the website below. I have used it many times. There are also other variations on the website.
Egg Drop Soup
Serves 2 - 4
4 cups chicken broth or stock
2 eggs, lightly beaten
1 -2 green onions, minced
1/4 teaspoon white pepper
Salt to taste
A few drops of sesame oil (if desired)
In a wok or saucepan, bring the 4 cups of chicken broth to a boil. Add the white pepper and salt, and the sesame oil if using. Cook for about another minute. Very slowly pour in the eggs in a steady stream. To make shreds, stir the egg rapidly in a clockwise direction for one minute. To make thin streams or ribbons, gently stir the eggs in a clockwise direction until they form. Garnish with green onion and serve.
Though egg drop soup is found in many variations in all kinds of Chinese Restaurants, my Chinese Chef freind in Sault Ontario assures me that traditional egg-drop soup is a mild chicken broth, almost bland, with a bit of chives, the eggs, and some salt and pepper (pepper is optional).
The recipe I use is simply a weak chicken broth (home made using chicken bones, and skins, celery, onion, carrots, salt), chives, and beaten eggs.
The key to developing those long strands of graceful egg is to mix the eggs very well, and to drizzle them into water that is not quite boiling. It must not even bubble. This allows the egg to set up in continuous ribbons, rathern than being broken up by agitating water.
If you don't want to go with the traditional, add other flavorings such as ginger, peppers, leeks, etc. And you can make the broth stronger.
But remember, the soup is served as a precurser to the main course and is used to whet the appetite and awaken the pallate. It is not the meal. And that's why traditionaly, it's served as the mild broth with eggs and chives.