To bind a carpet remnant to turn it into an area rug, begin by trimming the carpet to the desired size using a straight edge and utility knife. Trim away any fraying edges with scissors, and make sure that any corners are square. Purchase do-it-yourself carpet binding that has a corded edge fitted with an adhesive backing for easy installation.
Attach the carpet binding by removing the tape that covers the adhesive and pressing the binding against the back of the carpet. Make sure that the part of the carpet binding that is visible from the front is flush against the side of the carpet.
To bind around the corners, make a straight cut through the adhesive part of the binding so the cut aligns with the edge of the carpet. Do not cut through the corded edge of the binding that is visible on the front of the rug. Bend the carpet binding so it goes around the corner, and continue adhering the binding to the back of the carpet. After you finish binding the perimeter of the carpet remnant, cut the binding so the two vertical edges meet and are flush.
To permanently attach the carpet binding to the rug, run a bead of hot glue inside the channel between the corded edge of the binding and the carpet itself. Press the corded edge against the edge of the carpet to make the two edges bond. For best results, glue the binding to the carpet in small increments, so you can ensure that the binding fully adheres to the carpet before the hot glue cools.