Steam the lampshade, using a hot iron on the steam setting, to loosen the glue. Carefully remove the bias tape from the top, bottom and sides of the lampshade. When removing the bias tape, try not to tear the fabric that covers the shade.
Cut the fabric off the lampshade with a utility knife. Cut through the fabric only and not the inner shade. Cut along each rib of the lampshade to create individual fabric sections. Pull off the individual fabric sections. Pull gently to avoid tearing them.
Place the fabric sections on top of the fabric of your choice. Draw the outline of the fabric sections on to the new fabric, adding half-inch on all sides. Cut the outlines out.
Apply hot glue around the top edge of the first piece of fabric. Press the hot glue to the top edge of the ribbed lampshade. Wrap the edge of the fabric around the top rib by a quarter inch. Stretch the fabric down to the bottom of the shade. Apply hot glue along the bottom of the fabric and wrap it around the bottom of the shade by a quarter inch. Apply hot glue along the sides of the fabric and press it against the ribs. Cut away the excess fabric on the sides.
Place the second piece of fabric on the shade. Position it next to the first, gluing it on in the same manner. Overlap the edges of the two pieces of the fabric where they meet on the rib. Trim away the excess fabric. Repeat the process for the remaining pieces of fabric until the entire shade is covered.
Cut a piece of gimp trim the length of the lampshade plus 1 inch. Apply hot glue to the back of the gimp and attach it to one of the ribs of the shade, covering where the two pieces of fabric meet. Wrap the loose ends of the gimp around the top and bottom of the shade, a quarter inch on each side. Repeat the process using new pieces of gimp for each rib where the fabric meets.
Measure the circumference of the top of the lampshade. Cut a piece of gimp trim to match the measurement. Apply hot glue to the back of the gimp and wrap it around the outer edge of the top of the lamp, pressing the glue against the shade.
Measure the circumference of the bottom of the lampshade. Cut another piece of gimp and attach it to the bottom of the lamp in the same manner as the top of the shade.