Wash the stairs to remove dirt from the surface. Let them dry thoroughly before installing the mats.
Lay the vinyl mat on the center of the bottom step. Pull it up over the next step and mark with a grease pencil where the sides of the mat touch on both steps. This helps keep the mats evenly centered as you move up the staircase.
Add adhesive to the bottom step, covering any area where you want the mat to sit. This may include the inner ledge between each level or just the top of the step. Follow the instructions on the product for proper application.
Lie the mat down and line it up on your center marks. Push it back to cover the entire surface where you added adhesive.
Cut the mat along the back edge of the step with a utility knife or other form of blade if applying a separate mat to each step.
Run your hands over the mat to push out air bubbles.
Repeat this process until you cover all the stairs. Return to the bottom of the staircase and trim the starting edge so it's flush with the floor or step ledge. Examine the mats looking for loose areas. Reapply adhesive to any part of the mat that's not secure.