Pry the upholstery tacks or staples attaching the old fabric to the welting using pliers. The welting covers the inner staples attached directly to the frame. Once the inner staples are exposed, pry them out with pliers to release the fabric. Collect the tacks or staples in a container.
Remove the old upholstery fabric and batting from the furniture, making a note of how the fabric was folded around the corners. Place these aside to use as templates for the new fabric. Replace any sagging or loose springs. Turn the furniture on its side to provide access to its bottom. Remove the staples that attach the gauzy fabric to the frame and cover the springs. Locate the loose spring, snap it back into place and tighten the clip that holds it to the base of the furniture using a drill.
Spread the old batting on the new batting, and trace its outline. Cut along the lines using scissors. Spread the batting over the furniture's seat, in the exact location as the previous batting. Tuck the edges under the seat, and begin stapling the batting to the frame. Extend the batting along the furniture, stapling its edges to the wood frame.
Spread the new fabric face-down on a clean, hard surface. Lay the old pieces of fabric directly over it. Insert pins around the edges of the old fabric templates to hold them together, and then trace the outline of each piece of old fabric onto the new fabric using fabric chalk. Cut around the chalk marks carefully using sharp fabric scissors. Remove the pins and set them aside, along with the old fabric cutouts.
Position the new fabric over the furniture's frame, and join with upholstery tacks or staples. Start at the midpoint and work towards the corners, pulling the fabric taut to prevent folds. Fold the fabric at the corners the same way the old fabric was folded. Snip off frays or loose threads.
Cover any exposed tacks or staples with new welting. Insert decorative upholstery tacks to secure the welting to the furniture's frame. Use a rubber mallet to pound the tacks gently into the frame so you don't damage their decorative heads.
Place the furniture cushions on the new fabric. Allow two inches overall for seam allowance before tracing their outlines on the fabric. Cut along the outlines using sharp fabric scissors. Sew a slipcover for each cushion, with a zipper along one side, so it is easier to pull out and clean.