Clip the burnt ends of the carpet around the source of the burn, using sewing scissors. Depending on the depth of the burn and the type of carpet you have, this may be enough to improve the appearance of the burn.
Trim tufts from the undamaged carpet area around the burn. Keep trimming until the height of the tufts is as low as the depth of the burn. This will even out the appearance of the carpet and disguise the source of the burn.
Fill the hole with new carpet fibers if the burn is deep, such as that caused by a cigarette. Trim tufts from any leftover carpet segments you kept when the carpet was installed. Clip tufts from around the edges of the carpet if you have no excess carpet pieces.
Squeeze a small glob of glue into the carpet burn. Clean up any excess glue with a soft wet towel as soon as possible. If the excess glue dries, it can damage the appearance of the surrounding carpet.
Pick up the tufts of carpet you gathered earlier, using tweezers. Position the tufts in the burn hole and lightly press down so the tufts bind to the floor beneath. Keep adding tufts until the burn is no longer visible and the carpet has a smooth, even appearance.
Lay a clean white cloth on top of the tufts. This will soak up any glue residue that you may have missed before. Place a flat, heavy weight, such as a full paint can, on top of the cloth.
Leave the glue to dry and bond for approximately five hours. Remove the weight and examine the point of the carpet burn. Trim any fibers that are sticking up above the level of surrounding carpet, using sewing scissors.