Spruce up the Christmas dinner table so Grandma will pinch your cheek, impress the cute waitress at Olive Garden, or make the school cafeteria feel a little less like a prison mess hall with some of these napkin folds. Napkin art is a type of origami, but the medium is a lot more forgiving than paper and these folds are much easier then a Kawasaki rose.
I'll say 'fold diagonally' if I mean it; otherwise 'fold in half' means orthogonally. Since cloth napkins are usually square, or close to it, we won't have to discuss folding 'the long way' or 'the short way' or 'the hamburger way'.
If I were writing a book, I'd go into depth on the different types of material (cotton is better than a cotton/polyester blend), how much starch to use (just enough, but not more), and how the napkins should be ironed and stored to avoid unsightly wrinkles and creases. Since you'll mostly practice this in a restaurant where you don't control any of that anyway, I won't. I will note that the fanciest restaurants always seem to have the worst napkins for folding, and the restaurants that are just one step away from having a paper napkin dispenser on the table tend to use napkins that accept folds very well.
If you're from over the pond and giggle helplessly every time I say 'napkin', you may search/replace 'napkin' with 'serviette'.
Step 1: The Fan
Classic elegance. Adding some starch when washing or ironing the napkin gives crisper pleats.
Fold the napkin in half.
Starting at one end, fold over a pleat about one inch wide. Turn the napkin over and repeat with the same end. Turn and repeat. Stop about one fold after you make the remaining bit square.
Turn the napkin over so the stack of pleats is on the bottom. Fold the napkin in half the same direction as before, so the pleats are doubled on themselves.
Arrange the napkin so the original folded edge is on the top. Fold the remaining end down diagonally. About one inch will hang past the bottom. Fold this end under.
Hold the pleats together and set the napkin upright, so that very last folded edge is on the bottom. Release the pleats, which will fall to either side and create the fan. Do this with a flourish and a 'TA-DA!' if in front of friends. Try to remain calm and gracious during the thundering applause and shower of roses that will undoubtedly ensue.