A cigarette can easily burn the fabric of a couch if the hot end touches the fabric. In most cases the fabric will not catch fire because upholstery laws require fabric on furniture to be burn resistant. But the fabric will tend to melt or become damaged in a circle the size of the tip. Repairing this type of damage depends on the fabric type and whether you can harvest some of the couch fabric from elsewhere on the couch.
Vacuum and shampoo the couch to remove as much of the dirt and stains as possible. It is important when doing a mending repair that the fabric be as close to its clean or true colour as possible so thread colour and mending fabric can be matched more easily.
Examine the damage. If the edges are discoloured, use fine, sharp-tipped scissors to cut away the discolouration. If the opening is larger than a dime, look over the couch in areas such as deep inside the back of the arm. Look for extra couch fabric that is never seen under normal conditions. Cut a nickel sized piece of this fabric for a dime size hole.
Match the nap of the fabric. Many fabrics like microfiber have a nap or direction of the weave. When you run your finger across the fabric it will change colour slightly, based on the direction you rub.
Paint the edges of the cut burn hole with no-fray. No-fray is a product that stops a fabric from fraying along raw edges. Allow the no-fray 30 minutes to dry. Fold the patch in two and slide it into the hole. Use tweezers to unfold and position the patch in the right nap orientation and so it is evenly centred on the hole.
Thread a curved upholstery needle with a thread colour that matches the sofa as closely as possible. Bring the two ends of the thread together and tie a knot. Trim the excess thread away from the knot. Insert the needle through the hole and under the existing couch fabric 1/8 inch from the no-fray edge. Bring the needle up and pull the thread through.
Sew a crossover stitch across the no-fray edge. Bring the needle down into the patch and under, bringing the needle up alongside the first thread. Pull the thread through. Continue sewing small, tight crossover stitches around the patch, trying to blend the patch into the couch fabric as much as possible. Hide the end of the thread when you are done.
Smaller holes can be sewn across with the crossover stitch without the patch. Use the no-fray in the same way and remove any discolouration.