Examine the area of the chair where the fabric has pulled away from the frame. Locate the tacks, staples, ply grip or tack strip that was used to hold the fabric to the frame. If the fabric has pulled through or been torn around the nail heads or staples, the back of the fabric may need to be reinforced with interfacing that's ironed across the torn area, before nailing the fabric in place.
Cut fusible interfacing large enough to cover the damaged parts of the fabric. Position the adhesive side of the interfacing toward the back side of the fabric. Iron the area against a firm object, such as a wood cutting board, to fuse the interfacing to the fabric.
Remove the tacks or staples that have pulled through using pliers and a screwdriver. Fold the fabric to follow the shape of the chair and tack or staple it, using the interfacing to support the attachment points. You may need to fold the fabric under. Position the tack between the folds with the point toward the wood. Hammer against the outer fabric.
Remove any old or damaged tack strip or flexible ply grip. Use pliers and a screwdriver to pull out the tacks or staples holding the strips in place. Cut replacement strips of the same material with tin snips. Tack strips attach along straight edges. The fabric is pressed over the tacks, then the strip is rotated under. Hammer along the fabric that's over the tack strip to drive the tacks into the wood.
Attach a flexible ply grip to curved edges using a staple gun or tacks. Usually the ply grip is attached over welting. Welting is fabric-wrapped cord trim. Press the jaws of the ply grip half closed. Insert the fabric into the jaws using an awl. Hammer the outer fabric ply grip edge to press the grip together. Work from the center toward the sides and hammer evenly for a clean finish. The welting should hide the attachment area.