Start by making sure no one needs to go up or down the stairs for a little bit, then starting at the top. Sweep the stairs to remove any loose dirt. A paint brush or hand held broom can really help you get the back and side crevices.
Next, if you have an open railing, use a duster to clean in between and around each spindle.
Now that the loose dust and dirt is removed, move onto the risers. Shoes can scuff up the risers, if they're white, a little baking soda on a damp cloth or an eraser sponge will remove any marks. Regular wood risers can be cleaned just like the treads.
Again, working from the top down, use a mild vinegar and water mixture. A cap full of vinegar to a cup of warm water on a well wrung out cloth to wipe each tread and riser and immediately dry them with another soft cloth.
Never use commercial polishes on stairs, it will make them slippery and dangerous. Easy ways to make your stairs look their best! I'm Mrs. Fixit and it's just that simple!