Use a tape measure to measure the width of your staircase risers; record the measurements. Subtract 1 1/4 inches from each side to provide space for the carpeting to fold over and sit flat against the riser. Use a carpet knife to cut pieces of padding to fit these measurements. Use a staple gun to install the cut padding to the front of your top staircase riser so that it is short of the riser's edge by 1 1/4 inches on each side. Drive one staple into the edge of the padding every inch or so; also staple across its center portions so that no bubbles or loose patches remain. Use your hammer to drive home any staples that do not sit flush with the riser's surface.
Measure and record the width of the tread surface just beneath the top stair riser. Subtract 1/4 inch from this measurement, and cut your tack strip to size with a hand saw. Install the tack strip to the tread surface so that it is 1/8 inch short on each side. Use a hammer and nails to fasten one tack strip along the front edge of the tread, and one along its back edge.
Use the carpet knife to cut a piece of carpet to the height of your stair riser. Cut the same piece to the width of the riser and add 1 1/4 inch to each side. Use your awl and straight edge to create a fold in the back of the carpeting, 1 1/4 inch from each end. Fold the carpet over on itself and fasten it to the stair tread with 1/2 inch carpet tacks, hammering one in every few inches. Use your staple gun to fasten the upper and lower edges of the riser carpet in place.
Measure and record the distance between the back edge of your stair tread and the bottom edge of the stair tread bull nose where it touches the riser of the step below. Also measure the width of the stair tread from the underside of the bull nose at one side to the same point at the other side. Use your carpet knife to cut carpet padding to fit the measurements taken. Lay the padding into place starting at the back edge of the tread and overlapping the entire bull nose of the tread. Use the staple gun to fasten the padding in place along the back edge and under the bull-nose overhang. Use the carpet knife to miter-cut each front corner of the tread padding leaving no excess material. Use the staple gun to fasten the corner folds in place.
Cut the carpet to the same measurements as the tread padding. Lay the carpet in place in the same way, and use the carpet knife to miter the corners in the same fashion. Use your staple gun to hold the corners in place, then use a needle and thread to sew the split corners together and create a finished look.