Leftover carpet adhesive is almost worse than the undesired carpet on wood stairs. The entire look of the stairs can be ruined by yellow or brownish adhesive residue on the sides of the stairs. Regardless of whether you want to keep the wood bare or install carpet over the adhesive, you should remove the sticky debris because it isn't good for the wood. In fact, the longer carpet adhesive is on the wood, the harder it will be to remove.
Open all of the surrounding windows to create some ventilation. Removing carpet adhesive with white spirit or adhesive remover requires adequate ventilation, because both chemicals have toxic fumes.
Walk over and look at the carpet adhesive. If the carpet adhesive is brown or tan, a tar-based adhesive was used and you will have to remove it with white spirit. Yellow-looking adhesive indicates that a general adhesive was used and should be taken off with adhesive remover.
Apply a generous amount of either white spirit or carpet adhesive remover to the adhesive. Wait a few minutes for the chemicals to dissolve the adhesive.
Scrape the adhesive off with a scraper. Wipe the scraper and floor off with a towel as you remove the adhesive. Continue removing the adhesive from each step.
Remove any tacks or nails in your way with a pry bar. Sweep the stairs and throw the towel that you used in a plastic bag to place in the trash.
Wear gloves and a mask when removing old carpet adhesive.
Avoid smoking or getting a flame anywhere near the minimal spirits or carpet adhesive remover, because they are flammable.