Start by tracing a more flattering dress pattern out of your garment (you can use a dress you already own as a stencil), then sew along the lines. Cut away the excess side fabric then try it on. The chest and waist areas will probably be a bit loose still, so take in the side darts about a half an inch to make it more form-fitting.
Now, make the peplums by lining up your extra fabric and sewing it together into two long strips. Fold each strip in half and sew the layers together on every side except for one long side, which you should hem but not sew together. Fold it in half again to make a square, and then fold half of the top layer up to make a triangle on top of the square. Sew the peplums on to the waist of the dress.