Measure the length of the top stair step's tread, the horizontal part of the stair step, with a tape measure. Transfer the measurement to a nose cap, placing a mark on the nose cap's finished surface near the rounded edge.
Place the nose cap on a chop saw's cutting tray, keeping the cap's finished surface face-up. Slide the nose cap across the tray until its measurement mark lines up with the chop saw's blade guide. Cut the nose cap with the chop saw.
Set the nose cap on the stair step and measure the distance between the back of the nose cap and the stair's riser, the vertical kick plate at the back of the tread. Transfer the measurement to the finished surface of a tongue and groove flooring plank.
Position the flooring plank on the chop saw with its measurement mark aligned with the chop saw's blade guide. Cut the flooring plank to size. Cut each stair tread flooring plank, using the same measurement and cutting method.
Set each tongue and groove stair step plank in place between the top stair step's nose cap and the riser. The tongue on each plank slides into its neighboring plank's groove, forming a solid seam. Trim any long planks to size with the chop saw.
Remove the nose cap and tongue and groove flooring planks.
Spread hardwood flooring adhesive onto the stair step's tread with a 3/16-inch V-notch trowel.
Set the nose cap on the stair step's edge. Press the cap into the adhesive.
Secure the nose cap to the stair's tread with 18-gauge wood staples and a staple gun, driving a staple every 6 inches along the nose cap's nailing strip. The nose cap's nailing strip holds the cap's back edge -- the flat edge the flooring planks butt against -- down onto the stair tread.
Lay the tongue and groove flooring planks on the adhesive between the nose cap and the stair riser, keeping the tongue and groove seams locked together.
Press the tongue and groove stair covering into the adhesive with a floor roller, running the roller back and forth across the length of the stair step.
Install all of the tongue and groove flooring and nose caps on each stair step, using the same method as for the top step. Work from the top stair step down to the bottom step, completing one stair step at a time. Let the adhesive dry, according to the manufacturer's directions, before using the stairs.