Look at the back of the couch and under it to see if there is additional fabric to cut off and create a repair patch.
Place the piece of fabric over the burn hole, and cut the fabric to be slightly larger than the hole.
Cut away any burned fibers sticking up to make the hole flat. If the hole is deep, you may want to stuff it with a cotton ball to prevent the patch from being weak in the center.
Place fabric glue around the outside of the burn hole, then press the patch down on the couch firmly to seal it in place. If you have a couch with varying patterns, try to apply the patch so the pattern blends well.
Avoid sitting on that section of the couch until the glue has had adequate time to dry, usually around 12 hours.