Cut the remnant to size. Unroll the remnant of your choice out on a surface that is not prone to scratching, like a driveway or patio. Place the carpet face down so that you're working on the underside and use a tape measure to mark the dimensions you would like the finished rug to be, marking each corner with an X. Use a stiff measuring tape or yardstick to help you draw a straight chalk line from one X to the next. Carefully score the chalked line using a carpet knife. If the carpet knife does not cut all the way through the remnant, finish cutting it with a sturdy pair of scissors or carpet shears.
Heat an iron and place a towel down on the floor beneath whatever area of the rug you are working on. Working with a few inches of carpet edging trim at a time, fold it so that half is on the bottom of the remnant and half is on top. Place your hot iron on the trim and allow it to set for a few moments as the trim adheres to the carpet. Focus only on adhering trim to one side of the remnant at a time. Once it's attached around the entire rug on one side, flip it over and use the same technique to attach the trim to the other side of the rug.
Introduce another material as trim if you're looking for a customized look. Choose a colorful trim you've found in a fabric store, or a more masculine material, like leather. While these trims won't adhere to the remnant like the pre-glued carpet edgers, they can be sewn on with a heavy duty sewing machine. A simple straight line is all it takes to make a one-of-a-kind area rug trim.