Place the carpet cookie cutter tool on the area of the rug with the burn. Press down on the carpet and twist the tool to cut out a section of your damaged carpet.
Place the self-adhesive tape on the floor where the carpet was cut. Make sure you lay down enough tape to cover the hole.
Use the cutter tool on your extra piece of carpet. Turn the carpet piece over so that you are looking at the bottom. Press the tool down on the carpet and cut out a piece. This piece will be identical in shape to the one you removed.
Peel back the adhesive strip on the tape so that it is ready for your new carpet piece.
Lay down the new carpet piece on the tape and press down. Make sure it fits snugly around the edges and is even with your old carpet.
Run a comb through the edges of the new carpet piece and the original carpet. This will mix the fibers up so that you can't see the outline of the cut piece.