Cut out the damaged carpet section into a neat rectangle
Save the removed piece as a template if possible
Cut a matching patch from a leftover carpet remnant
Match the carpet pile direction before cutting
Trim the patch slightly to fit the opening
Remove loose fibers and debris from the subfloor
Apply carpet seam tape or adhesive under the opening
Place the patch into the opening with pile direction aligned
Press the patch firmly into place
Blend the seams by brushing the fibers together
Trim any uneven fibers with scissors
Weigh down the patch until the adhesive sets
Vacuum the repaired area after it is secure