Cut the cigarette burns from the sofa fabric with small scissors. Remove only the burned areas of the fabric and cut any loose threads.
Measure the holes in the sofa. Cut replacement patches from material on the underside or on the back near the bottom of the sofa. Cut the replacement pieces one-quarter inch to one-half inch larger than the holes.
Pour fabric glue onto a toothpick, and apply the glue into the hole in the sofa. Pick up the patch with tweezers and apply a tiny amount of the glue around the edges of the patch.
Place the patch into the hole, positioning it with the tweezers to match the pile or pattern in the sofa.
Tear off a piece of plastic wrap and place over the patch. Put a heavy book or other object over the plastic wrap and leave for two hours, allowing the patch time to bond.