Draw the puppet pattern you want to use directly onto the cloth, using the wrong side of the fabric. Use a black marker or a dark pen to make the mark.
Place a second piece of the same fabric below the one with the pattern. Pin the two right sides of the pieces together. Sew around the outline of the puppet, through the two pieces of fabric. Backstitch the beginning and the end of the stitching.
Cut around the sewn puppet pattern mark, leaving a 1/2 inch seam allowance. You will cut on the other side of the heads of the pins.
Turn under the open edge of the puppet and stitch it so it will not fray. Turn the fabric inside out and press firmly with a hot iron to make the seams straight.
Decorate the new puppet appropriately using items you have at hand. Some ideas are markers, buttons, ribbon or small jewelry stones from cast-off pieces.