Here's how I have made baskets.
1. My original form was made by covering most of an unsharpened pencil, including round and octagonal shapes, with a piece of plastic wrap and fastening it in place with a rubber band.
2. Using an old credit card or a piece of card I smooth tacky glue over a small square of finely woven fabric like lawn, or many-times-washed old handkerchiefs, the finest hardanger or aida cloth and shape it over the end, holding it in place with another rubber band until dry.
3. I paint the basket while it is on the form, leave it to thoroughly dry, then cut away the excess fabric. The finished top edge and the handle are made by coating with glue two threads pulled from the material's edge, twisting them together, and wrapping them around the pencil to dry.
I have since used various shapes that suggest the type of basket I want - oval, oblong, square, etc. gluing them onto the tip of another pencil or a dowel for holding, if necessary. For certain baskets I have also used special papers or paper cocktail napkins, and decorative fine threads from my stash, as well.
I keep the forms, fabric, threads and finest silk ribbon for handles and trims, and extra rubber bands together and like to make a variety of baskets at one time, standing them in a cup to dry. Sometimes I don't trim them or add the handles or trims until later when I want them to follow a certain style or color scheme.