Wash the burn with a soapy water solution. This will remove any charred bits and help lighten the spot. Allow the spot to dry fully --- about 24 hours --- before covering.
Arrange furniture to cover the burned spot. Move couches, chairs, end tables or lamps to cover spots located close to a wall.
Place a rug over the carpet burn. Large burn spots or those in the middle of a room will probably require an area rug for full coverage.
Trim the burn marks with scissors from the burnt carpet. Apply a few drops of superglue to obscure the melted carpet fibers.