Measure the width of the stairs with a tape measure to learn the how wide to cut the carpet. Or if you desire only to cover the main wear area of the wood steps with carpet, measure the desired coverage area.
Cut the indoor/outdoor carpet to width with a pair if industrial quality scissors or a carpet knife. Lay the carpet down the stairs to be sure the width of the carpet is correct before proceeding.
Fill a staple gun with staples and close it up. Staple the top end of the indoor/outdoor carpet to the horizontal surface of the topmost step to hold the carpet in place. Secure that top edge of the carpet by installing a wooden or metal transition strip so the top edge of the carpet will not separate from the top wood step.
Fold the carpet down the rise of the first step and use the staple gun to secure the carpet around the corner of the step. Staple the carpet to the rise again near the corner where the rise of the first step and the run of the second step meet. Staple the carpet to the run of the second step near the corner as well.
Repeat Step 4 for each subsequent step until the carpet is fully stapled into place.
Fasten the bottom end of the carpet into place with a thin, narrow strip of wood, like a piece of lath wood. Pre-drill holes in the wood at each end and in the middle of the so the wood will not crack and split where the screws are applied. The wood should be pre-finished with at least one coat of polyurethane so it will last longer.