Mark a small circle surrounding the burnt area of the fabric. Cut out the circle of fabric using cuticle scissors.
Use the cut circle as a guide to mark a slightly larger circle from back or bottom of the couch, wherever you find identically patterned fabric that you normally don't see. Cut out the larger circle.
Place the large circle of fabric over the hole where the cigarette burn used to be. Match the pattern of the circle to the pattern around the hole. Glue the circle to the fabric using fabric glue.
Lay wax paper over the glued fabric. Place a heavy book over the wax paper. Let the glue set overnight before removing the book and waxed paper.