You can install hardwood on floors using either prefabricated hardwood stair treads and risers, or by using the same hardwood as your flooring and adding stair nosings.
You can start at the top or bottom of the stairs. Regardless of whether it was a floating, nail, or glue down installation, all hardwood installed on stairs should be glued and nailed for safety. Holes can be filled with a matching wood filler after installation.
Check out pages 66-71 of this installation manual for instructions on stair installation.
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