Remove carpeting or runners from the stairs. Clean all nails, staples and glue residue from the stair treads. If the front edge of the stair tread is rounded, use a circular saw to trim off the rounded edge. Vacuum thoroughly to remove any dust or dirt from the treads.
Install stair nosing to the squared front edge of the stair tread. Use glue on the inner section of the stair nosing. Tap the nosing with a rubber mallet to ensure full contact with the stair riser. Secure the nosing to the stair tread with screws and a screwdriver for additional safety.
Measure from the stair nosing to the point the riser intersects with the tread, using a tape measure. The stair nosing has an opening the laminate flooring will slide into; include this in your measurement. The laminate plank that will install against the riser likely will need trimming. Slide a full piece of laminate under the stair nosing tongue side out, the remaining distance is the width the second piece will be trimmed.
Lift the pieces of laminate when you are satisfied with the fit and apply glue to the stair tread. Slide the full-width piece under the nosing and then the trimmed piece will butt up to the stair riser. Glue laminate to the riser, using a full piece nearest the stair tread and the trimmed piece up to the nosing. Continue working downward on the stairs until all treads and risers are covered with the glued laminate.
Install quarter-round to the intersection point of the riser and stair tread to cover the gap. Install shoe molding to the first riser at the bottom of the stairs at the point the riser meets the landing. Avoid walking on the glued laminate for 24 hours if possible.