The main cuase of carpet burns is usually cigarettes, or coal from bbq or smoking shisha pipes. Repairing carpets with this kind of burns involves cutting out the affected area and then replacing it with a spare piece of carpet which has been cut to fit. The new piece carpet is then glued into position. If the burn is small, the burnt carpet fibers can be cut with scissors. For larger burns, you may have to replace the area with a new piece of carpet. Make a paper template slightly bigger than the hole. Cut out the damaged section using your template. From an unnoticeable corner (or another room), cut the template-sized carpet with a sharp knife. Now, fix it in the hole and seam the edges.