Why drape? Because if we don’t use draping techniques on our doll’s costume it will look unrealistic and rather shapeless. In real life, fabric is shaped to fit our bodies and the fabric drapes from the weight of the material. On a small scale doll the fabric has hardly any weight so we have to simulate the way fabric looks in real like.
Draping is the method of pinning folds and placing fabric in the position you want it, so that the fabric maintains that shape when it dries. To wet the fabrics, you use a water plus starch mixture, spray starch or light misting of inexpensive hairspray.
Check your fabric: As a rule, if you take a tiny sample piece of a natural fiber and dip it into a starch plus water mixture, the water will be absorbed; on synthetic fibers it beads up and is not suitable for draping. Synthetics work best for tailored costumes.
To begin, make a pinning board from a piece of 12 inch by 12 inch Styrofoam, ceiling tile or thick Foamcore and cover it with plastic wrap. You need some insect pins or silk pins and waterproof glue (such as Fabric Tac). To dry, you can use a blow dryer or let the costume day in the air. Place your doll in a stand or on the item where it will sit. Cut a corner of a sandwich bag to cover the head and fasten it in place. Begin constructing the garment.
To achieve the look of fabric falling in folds, you begin by gluing and sewing the garment parts to the doll so that it is tight and will hold the shape you intend after you wet it and it has dried. Small scale doll costumes are constructed in segments, from the inside out and bottom to top. As you construct each part, you glue, sew, pin and pleat the fabric to control the shape, reduce the bulk, and to drape. The fabric loses the softness of a sewn garment but we are more interested in the final appearance of our OOAK dolls. Other things doll makers use to control shape are tiny sewn-in weights and wire incased in hems.
There are lots of tricks and tips to draping. You will find information on-line and in books and videos.