Open all of the surrounding windows to create some ventilation. Removing carpet adhesive with mineral spirits 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 mineral spirits. Yellow-looking adhesive indicates that a general adhesive was used and should be taken off with adhesive remover.
Apply a generous amount of either mineral spirits 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.