Apply Fray Check, a clear liquid-plastic solution, to the edges of the tear to prevent any further raveling. Allow the Fray Check to dry.
Thread and knot the curved needle with thread that matches the ripped fabric.
Fold the loose side of the tear under.
Push the needle through the underside of the folded fabric at one edge of the tear.
Push the needle down through the taut fabric, directly across from where the needle exited the loose fabric. Angle the needle slightly diagonally from where you entered the fabric and catch the fold of the loose fabric as the needle comes back up. Pull the thread taut so that the folded edge now covers the ripped edge.
Continue making very small stitches across the tear in this manner.
At the end of the tear, knot the thread by making a loop, then threading the needle through the loop twice. Pull it taut.
Bury the thread by sticking the needle back through part of the stitching you have just done.
Cut the thread close to the repaired tear.