In the western tradition, a soup spoon is a piece of flatware about as long as a tablespoon but with a round rather than an oval bowl. At a fancy meal with a daunting array of glittering silverware, the soup spoon is usually on the far right side of your plate; that's because you utilize your utensils from the outside in, and in the west the soup course usually precedes the main course.
There are rather strict rules of etiquette surrounding the eating of soup in the west, and it may take some practice to pull off soup eating in a manner that would make Dear Abby proud. Basically, you're supposed to dip the soup away from you, allowing the soup onto the spoon from the far side, then sip the soup in a genteel (read: silent) manner from the near side. Don't put the whole spoon in your mouth, and for heaven's sake don't slurp. If the soup is too hot, just wait till it cools; it's considered gauche to blow on it. It's okay to tip the soup bowl away from you to get the last of the soup out of the bowl. If you pause while eating your soup, just leave the spoon sitting in the liquid; once you're done, place the spoon on the dish under the bowl.
Whew! That was complicated. Now, go to Asia, and forget all that you've learned about soup and soup spoon etiquette.
The Asian soup spoon is usually a short ceramic spoon with an oval bowl. The bowl has a flat bottom, so the spoon can sit with the bowl resting on the table and the handle in the air, but don't do that. Instead, rest it upside-down on that little flat bowl-thingie that you use to mix sauces in, or in your bowl of soup if you think it won't slide into the soup. Soup can be eaten with the soup spoon alone or with chopsticks and spoon (in which case chunks of tofu or noodles or whatever are often removed from the soup with chopsticks, placed on the spoon, and thence conveyed to mouth). Alternatively, there may be no spoon in sight, in which case you're free to drink directly from the bowl. Many Asian cultures consider loud slurping and even burping during eating to be a sign of enjoyment of the food, and not a horrible faux pas at all, so you can make all the noise you like. Your mom wouldn't like it, and Ann Landers would have a fit, but we're young and free and we want to live a little, right? So go for it.