Measure the length of the stair tread's edge where the stair nosing will go.
Measure and cut the stair nosing to fit on the top tread(s).
Install the stair nosing so that the curved part fits snug against the stair riser stepping down from the landing. Apply a thin, serpentine bead of construction adhesive to the stair nosing and press it into place. Finish with finishing nails.
Install the first piece of hardwood flooring (using whichever method you used for the rest of the floor such as nail-down, glue-down or tongue-in-groove) so that it butts against the back of the stair nose -- your stair nose is the "first piece" of flooring on your landing.
Stagger the boards as you have done on the rest of the floor, cutting the boards as needed for the last row or for the first board in a row. Follow the instructions for staggering the seams. For example, if you are supposed to stagger the seams on your floor by having the second board be one-half the length of the first board and so on, continue this in the landing.