Locate a left over carpet remnant from the original install. If remnant is not available, look for a closet or other obscure location that has the same carpet in it. Cut it out of the floor using a carpet cutter or utility knife.
Place a straight edge on the floor next to the thread bare area as a guide and cut through the carpet until you reach an undamaged area. Be careful not to cut through the underlying padding. Use the straight edge to cut around the three other sides of of the threadbare area so that you create a square cut-out. Discard the center portion of carpet.
Cut three to four pieces of carpet tape to the same length as the carpet cut-out. Peel the protective backing off of one side and press the tape pieces onto the carpet padding. Once secure, peel the top paper off to reveal the adhesive.
Place a tape measure in the cut out area of the floor and measure the exact length and width.
Turn the piece of carpet remnant over so that the back faces upward. Draw the measurements of the cutout area onto the carpet remnant using the straight edge and a pencil. Cut along the marked areas using the carpet cutter.
Flip the carpet remnant piece right side up and turn it so that the pile faces the same direction as the carpet on the floor. Place it into the cut-out on the floor aligning the edges perfectly. Press the piece down firmly to secure it. Then run your hand over the carpet surface to blend the pile together and disguise the repair.