Choosing the Paint
Stairs are part of the floor, so you need durable paint that won't chip or scuff easily. For an exterior staircase, you can choose an oil- or latex-based porch and floor enamel or a semitransparent stain. You should stick to water-based products when painting interior stairs. Don't despair if you can't find a floor enamel with the color you want; you can protect any finish from foot traffic by coating it with clear polyurethane. Along with the fact that they contain lower concentrations of VOCs, water-based products dry faster than oil-based ones, and using them reduces the likelihood of damage from premature use of the newly painted stairs.
Clean Before You Paint
The need to clean before you apply paint is axiomatic -- but it's magnified when you're painting stairs, because there's more dirt and it's more likely to cause problems. Vacuum thoroughly, using an attachment with a narrow opening that can suck dirt from small crevices, and then wipe all surfaces and crevices with a damp cloth. If your stairs already have a glossy finish, wash them with a strong detergent -- such as a solution of 1/2 cup trisodium phosphate per gallon of water -- to cut the gloss and aid paint adhesion. Let everything dry, and then sand lightly with 220-grit sandpaper. Wipe off the dust before painting to ensure adhesion.
Start at the Top
If your staircase has a railing, paint it before you paint the steps -- it's a job that may require two days of standing on the treads, and you don't want to do that right after you've painted them. When it comes to the treads, always paint from the top down -- that way you can see the risers and the critical area just under the tread nosing, which is virtually impossible to paint from above. If you need to use the staircase while the paint is drying, paint every other tread and wait for them to dry for two days before you paint the other ones.
Using Masking Tape
You'll need masking tape if you use more than one color to make stripes or to differentiate the treads from the risers. Use blue or green painter's tape -- preferably a brand with a polymer adhesive that prevents seepage. Seepage can occur even if you use high-quality tape, though, unless you employ a simple trick that works especially well when painting stripes. Paint the base coat, and let it cure for 24 to 48 hours. Then lay the tape to form the stripes. Paint over the tape with the base color and let the paint dry; it seals the tape edges, so when you paint the stripe color over that base coat, it won't seep. When you remove the tape, the stripes will have crisp, clean edges -- guaranteed.