You will need Vilene watersoluble stabilizer, embroidery threads, preferably polyester ones, and a small button. If you want to make a fabric vest, you'll also need scraps of fabric big enough to be hooped in the large hoop. Felt, either wool or polyester, is very good for the purpose.
To make the FSL vest, hoop 2 layers of Vilene watersoluble stabilizer and embroider all three parts of the vest one by one. Wash away the stabilizer in warm water and leave to air dry. Press the parts with steam.
To assemble, stitch together the shouder seams. Press the seams open. Then stitch the side seams and press them open. Attach the button. The vest is ready and you can put it on the doll.
To make the vest on fabric, hoop a piece of fabric with 1 layer of water-soluble stabilizer. Skip the first color and start embroidering with the second color. Embroider all three parts of the vest one by one, skipping the first color. Wash the stabilizer away in warm water and leave to air dry. Press with steam.
If you work with felt, you can try to work without stabilizer, just be sure that the hoop is tightened properly.
Cut out the parts, leaving 1/4" seam allowance for the shoulder and side seams, and cut as close to the threads as possible along the hem, front and neck line.
To assemble, stitch together the shouder seams and press the seams open. Then stitch the side seams and press them open. Attach the button. Cut the button hole. The vest is ready and you can put it on the doll.