Measure the first stair tread's width and subtract the carpet's width from this measurement. Divide this number by two. Transfer this number to each stair tread, measuring from the stair tread's left side toward the center and make a line. This line indicates where the carpet's left edge will be located.
Lay a strip of double-sided carpet adhesive on each stair tread, directly in front of the next stair's rise. Make each strip of tape slightly narrower than the carpet's width so it will not be visible at the carpet's edges. Leave the paper backing on the tape.
Unroll the carpet up four stairs. Line up the carpet's end with the bottom edge of the first stair's rise. Drive a staple through the carpet and into the stair rise every 3 inches. Hold the carpet tight against the first stair's rise, and drive staples through the carpet, every 3 inches, below the first stair's tread.
Center a knee kicker on the carpet on the first stair's tread, about 2 inches in front of the second stair's rise. Hit the knee kicker with your knee to pull the carpet forward. Do not pull the carpet so tight that it pulls out the staples. Reach underneath the carpet and peel off the tape's paper backing.
Press the carpet onto the tape. Push the carpet into the corner where the first stair's tread meets the second stair's rise with a carpet tool and rubber mallet. Drive two staples into the carpet and corner, one near each of the carpet's edges, to help hold the carpet in place.
Push the carpet against the second stair's rise. Drive a staple through the carpet and into the second stair's rise, every 3 inches, below the second stair's tread. Place the knee kicker on the carpet covering the second stair's tread.
Pull the carpet forward, over the second stair's tread. Peel off the tape's paper backing and press the carpet down onto it. Push the carpet into the corner with a carpet tool and rubber mallet. Staple the carpet in the corner with staples spaced 3 inches apart.
Smooth the carpet against the third stair's rise and drive staples through it underneath the third stair's tread. Continue to work your way up the staircase, taping and stapling the carpet to each stair. When you reach the top of the stairs, cut the carpet flush with the landing using a sharp utility knife. Staple the carpet underneath the landing with staples placed every 3 inches.