Soup can be served in a wide, shallow soup plate or a deeper soup bowl. If you're eating from the former, the spoon should be rested in the soup plate in between bites and when you are finished eating. If it is the latter, always rest the spoon on the plate below the bowl, not in the bowl itself. If the soup is served in a cup with handles, it is appropriate to lift the cup up and sip from it directly, but use your spoon to eat any solid ingredients like vegetables or noodles.
Want to see proper soup-eating in action? Check out the video below. (If "action" isn't how you'd describe a video of a woman demonstrating how to politely eat soup, you may want to skip it.)
This etiquette applies to soup-eating in the United States, but there are many other ways to eat soup around the world. Do you come from a culture that has different rules? How do you eat soup?