Cut the carpet fibers that are burned by using a pair of small scissors. Hair clippers or any sharp scissors work well. It is only necessary to cut the tips if it is just a surface burn.
Rub a scouring pad over the cut fibers to fluff them up.
Vacuum over the area to remove the residue from the cut fibers.
Fold an old towel and place it on your work surface. Another option is to use a piece of old plywood. This prevents the utility knife from scratching or cutting a gouge in it.
Set the carpet scrap on top of the towel or plywood.
Place a drinking glass or another object that may be used as a template over the burned area to ensure the patch covers the entire area. Allow at least an inch or two around the burned area for the patch. It is less difficult to work with a 3- to 6-inch patch than one that is smaller.
Set the drinking glass or other object upside down on the carpet scrap and cut around it with the utility knife.
Place the patch over the burned area on your carpet.
Tape the patch over the damaged carpet with strong tape.
Cut around the patch into the burned carpet.
Remove the burned section of carpeting and set the new patch down inside it to make sure it fits correctly. Lift it up and flip it upside down.
Apply a carpet seam adhesive to the outer edges of the patch and in the middle. Set it down on the floor with the adhesive side down and press the carpet patch firmly with your fingers. Another alternative is to use double-sided carpet tape on the floor then press the patch in place.
Vacuum over the area once the carpet dries, according to the carpet seam adhesive instructions. If you use the double-sided carpet tape, you can vacuum the area right away.