Put a dust mask on. Run an orbital sander on the upper surfaces of the steps, starting on the top step and working down. Sand the vertical risers of the steps with sandpaper and a sanding block.
Sweep and vacuum up the sawdust, dirt and other debris from the sanding process.
Wipe the exposed wood surfaces of the steps with a rag dampened with mineral spirits. Work from the top step down. Repeat a second time to ensure you've cleaned the surfaces thoroughly.
Paint or stain the steps, working from the top steps down. If you're staining the treads of the steps and painting the risers, do the staining first. Let the stain dry completely, mask off the stained wood with masking tape and paper, and paint the risers of the steps.
Remove the masking tape and paper when the paint is completely dry.
Paint the wood-stained surfaces with a urethane coating to add a further layer of protection. Be sure to let the urethane dry completely before allowing traffic on the steps.