Turn the carpet over so that the bottom side is facing up.
Sketch out the shape of the rug you want on the underside.
Cut along the pencil line using a utility knife, keeping your cut as clean as you can. Cut slowly to keep the edge even.
Trim the edges of the cut-out carpet with a pair of heavy scissors, removing any jagged edges or frayed fibers.
Lay the carpet-binding tape adhesive-side up on the floor. Carpet-binding tape has a fiber binding edge and an adhesive strip below it.
Remove the plastic backing that covers the adhesive.
Turn the carpet right-side up and press the edge of the carpet to the adhesive, getting the edge of the carpet as close to the binding edge as possible. Start the binding tape along the middle of one side.
Continue pressing the carpet to the tape, overlapping the tape when you need to go around the corner.
Snip the carpet-binding tape using the scissors when you reach the place you started, bringing the two ends to butt up against each other.
Apply a small dot of hot glue using a glue gun to the crevice between the binding tape and the carpet to secure the carpet to the binding further. Place one dot every 4 to 6 inches.