Get a patch of fabric that matches the upholstery fabric. Measure the tear. Cut the patch so that it is 2 inches longer and 2 inches wider than the tear. Insert the patch into the tear. The patch should lay flat on the inner cushion and completely cover the area so that you cannot see any cushion through the tear.
Secure the patch in place with straight pins.
Strengthen frayed edges of the tear with Fray Check. Fray Check is a clear liquid available in notions departments. Dab a small amount of Fray Check on the frayed edges of the tear. Allow to dry for at least 30 minutes.
Use strong, thick polyester thread to mend the tear. Weaker thread may break easily under the use of a couch or chair. Choose a color as close to the upholstery color as you can find. Thread a curved upholstery needle, or a straight needle if you prefer. Many find the curved upholstery needle easier to use when mending torn furniture.
Stitch the tear shut the same way you would hand-stitch any fabric tear. Start at one end, push the needle through the fabric and knot. Stitch down the length of the tear using a slip stitch, which is practically invisible. Knot the other end.
Remove the pins.