For the most part, you want to make noodle soup by adding cooked noodles to cooked soup just before serving. This maintains the integrity of each and keeps everything from turning into an undifferentiated, starchy mess. Undercook the noodles slightly (they’ll finish cooking in the hot broth); you can even prepare them ahead, rinse them in cold water to stop the cooking and remove the surface starch so they don’t stick together, cover, and refrigerate until you’re ready to use them.
Often, it’s better to cook the noodles right in the soup, to maximize the body-building and flavor benefits. Soups made this way have only a narrow window of time before serving — the noodles start to break down quickly — but I maximize that window by using the sturdiest noodles, or frying them first to make them a little less soluble.