Stripping Old Paint
If you're removing carpet, painting new stairs or painting over varnish, you don't have to worry about stripping the finish. If your stairs have several coats of old, peeling paint, though, you may want to remove it, and a light-duty furniture stripping compound isn't going to do the job. Use a heavy-duty paint stripper -- you can tell it's heavy-duty because the container is heavy, which means the stripper contains a high concentration of caustic methylene chloride. Wear old clothes, gloves and a respirator when using it. Spread it liberally with a paintbrush; wait for the paint to bubble, and then scrape with a paint scraper. It may take several applications to do the job; rinse with water when you're done.
Cleaning and Sanding
You may not have to strip them, but you should always clean the stairs thoroughly first by vacuuming away dust and dirt, and then washing the old finish with a solution of trisodium phosphate detergent and water. This strong detergent gets off any grime that could inhibit paint adhesion and it etches the finish. Sand unfinished stairs -- or ones you stripped -- with a progression of sandpaper grits. Use 80-grit to remove stripping residue and to remove nicks and gouges from the wood, and then sand with 100-grit and finish with 120-grit paper. A palm sander makes sanding with coarse grits easier, but do the final sanding by hand, following the grain of the wood.
Paint the Railing, Mask and Prime
You may be planning to paint the railing along with the stairs, and if so, paint the railing first so you don't have to protect the stairs with a dropcloth. Once the railing has dried, you can remove any spots on the steps with sandpaper and mask the edges of the stairs against both the walls and railing with painter's tape. You're now ready to apply primer, which is a necessity on bare wood or if you're painting over oil-based paint with latex. Use a high-solids latex floor primer and, to extend the coverage of the paint you're using, tint the primer a similar color.
Paint the Treads and Risers
The most durable paint for interior stairs is latex floor enamel, but it comes in a limited variety of colors. As an alternative, you can paint the treads and risers with conventional latex wood enamel and add one or two protective coats of polyurethane floor finish or varnish. Always start at the top of the staircase and work your way down. If you need to use the staircase while the paint is drying, paint alternate stairs, wait for the paint to dry, and then paint the others. Use a synthetic-bristle paintbrush with latex paint and stroke with the grain of the wood, starting and ending your strokes as close to the ends of the steps as possible.