Use the power sander and heavy sandpaper to sand each of the stairs, taking off a layer of the wood.
Repeat the sanding process with fine sandpaper, making the surface completely smooth. Vacuum well.
Use a paintbrush to coat the top stair in wood stain, brushing it on heavily. Let it sit for minute, soaking into the wood. Wipe up the excess stain with old rags.
Skip the next stair down, then stain the stair below (i.e., the third stair from the top). Repeat, staining every other stair, so the stained and unstained stairs alternate.
Let the stain dry overnight, walking only on the unstained stairs during that time.
Apply varnish to the top stair (the one that's stained) in a thin, even coat, brushing it on slowly. Repeat for each stained stair, while leaving the alternate, unstained stairs alone. Let the varnish dry overnight, walking only on the bare stairs during that time.
Sand the dried varnish lightly with extra fine sandpaper, dulling the shine. Apply a second layer of varnish to the stairs you've been working on (continuing to leave the alternate stairs bare). Let it dry. If a third coat is desired, then lightly hand-sand the second coat before applying the third. Let the final coat set for 24 hours.
Put a small piece of masking tape on each stair that's been stained and varnished, so you'll know which are already finished (and, therefore, can be walked upon), while you're staining and glossing the alternate stairs. Follow the same procedure to stain and gloss the alternate stairs.