Lay the upholstery fabric over the chair. The placement of the fabric depends on whether you are upholstering the seat corners, the back or the arms, but the fabric should be at least 3 inches longer than needed regardless of the area.
Tuck the fabric in along the vertical edge of the corner, similar to wrapping a gift. Pin the fold in place using upholstery pins.
Repeat the tuck on the vertical edge of the opposite corner, pinning this fold in place. Smooth out the fabric inside the tuck so it lies flat between the two corners and doesn't create a lump.
Thread a curved upholstery needle with heavy-duty upholstery thread in a color that matches the fabric. Knot the end of the thread securely.
Sew the fold together using small, even stitches. Camouflage the stitching by placing it where the two folds meet from the tucked fabric down the vertical edge of the corner.