Cut the torn area out of the carpet with a circular carpet patch tool, also called a cookie cutter. Remove the circular piece of torn carpet.
Attach a hose attachment to your vacuum and vacuum the exposed hole to remove any debris that may interfere with adhesion.
Cut out enough pieces of double-sided adhesive patch tape to fill in the hole. Fold the tape so one side will stick to the sub-floor and the other side is ready to adhere to the replacement piece of carpet.
Cut out a piece of the carpet remnant with the cookie cutter tool. Stick the carpet patch into the hole and press down on it to adhere it to the tape.