Trim the tops of the burned carpet fibers using a pair of small, sharp scissors. Only cut the tips of the fibers to prevent making an indention in the carpet.
Remove any remaining burned areas on the fiber by scrubbing the tips with a scouring pad. This loosens any remaining charred tips.
Vacuum the carpet to remove any residue from the carpet repair. This fluffs up the carpet so that the damaged area is hardly noticeable. This technique works best on areas where the burn is not very deep and only damages the very top layer of the fibers.
Cut around the black area with a utility knife so that you remove the burn spot and a couple of inches on all sides. Don't cut so deeply that you score the padding.
Lift up the burned carpet section with your fingers.
Set the damaged carpet on top of your carpet scrap so that the nap on the carpet matches up with the nap on the scrap. Do this on a piece of plywood or a padded area to prevent cutting into your work surface.
Cut around the damaged carpet with the utility knife.
Squirt a stream of carpet adhesive on the backside of the carpet scrap. Do this near the edges and in the middle. Double-sided carpet tape is also available at hardware, home supply and other places that sell carpeting. Simply peel off the backing and attach it to the carpet back.
Look at the area that requires a patch to determine which way the nap is running. Set the carpet patch down into the hole so that the nap matches.
Press the patch firmly in place with your fingers. Place a book or other heavy object on the patch until the adhesive dries. Read the directions on the label to determine the drying time.
Vacuum the area once the adhesive dries to fluff up the carpet.