Remove the original stair coverings using whatever technique the original installation of the covering necessitates. Pull up carpeting, for instance, which generally installs with adhesive and small tack strips at the edges, by hand, or use a hammer to remove the nails from hardwood stair coverings.
Scrape off any coatings left on the wood surface after removal of the original floor covering. Go over carpet adhesive, for instance, with a paint scraper, removing the largest chunks of adhesive from the stairs, and then go over the adhesive on the stairs again with medium-grit sandpaper until the surface of the stairs feels smooth. You can remove paint from any type of stair surface, such as wood or cement, using this same technique.
Prepare the stairs for the new type of flooring that you want to install. If you plan to repaint or paint concrete or cement stairs, apply a waterproof masonry sealer to the stairs prior to applying paint, or apply paint primer to wood stairs. If you want to install hardwood or laminate on the stairs, put down a waterproof underlay to prevent moisture issues, using the self-adhesive strips, or apply carpet padding to the stairs if you want to lay carpet.
Put down the flooring according to the manufacturer’s instructions. Lay carpet over stairs in one long strip whenever possible, placing tack strips at the back bottom corner of each stair and tucking the carpet into these back corners of the stairs until the carpet fits tightly against each stair and holds on the tack strip. Apply hardwood or laminate flooring over stairs by laying enough planks to cover each stair, cutting the planks down with a circular saw where necessary and securing the planks to the floor with nails in the case of a wood staircase, or with adhesive in the case of a masonry staircase.