Some styles of folding napkins are buffet-style, silverware roll, knot fold and fan fold. You can also fold napkins into creative shapes or roll them up in napkin rings.
For a buffet-style napkin, fold the napkin into quarters, roll each layer of the open corner down, tucking each rolled corner under the one above it, turn the napkin over and fold the left side 1/3 of the way across the back. Fold the right side back to meet the left side, then flip the napkin over and insert the silverware.
For a silverware roll, fold the napkin in half diagonally, then fold both corners in and roll the napkin. For a knotted napkin, fold the napkin in half diagonally, roll the napkin flatly and tie it in a knot. For a fan, fold the napkin one inch back and forth and secure the bottom with a napkin ring.