Measure the length and width of the turnout.
Add this measurement to the measurement for the rest of the stair and riser.
Lay a piece of carpet over the turnout stair that is wider than the stair.
Cut the carpet with a sharp utility knife or carpet knife so that the pieces are the exact length of the riser, tread and the nosing. For a width measurement, add about 1 inch to the measurement so that you can fold under the side or wrap the carpet around the turnout.
Staple, tack or glue the carpet in place, and trim any excess to conform to the turnout.