Measure the width and length of each tread from top to bottom, and write them down. No two stairs are exactly alike, particularly if the house is old and has settled over the years. Go to your local home -improvement center and order the tread covers. They come in standard sizes, but you can have them custom cut at the store if you don't have a tablesaw. Mark each stair as it is cut.
Stain the replacement treads to match the hardwood in your home. Brush stain on with a paintbrush and wipe off excess with a soft cloth. Be sure to work with the wood grain, not across it. Allow it to dry according to the specs on the can. Sand lightly between coats and apply as many coats as you need to get the right color. Finish with polyurethane to seal the wood against scratches and scuff marks.
Cut back each old stair tread flush with the riser with an electric jigsaw. Sweep up the sawdust, and wipe down with a damp cloth.
Apply construction glue to the back of the bottom stair tread cover. The glue comes in caulking tubes and is simple to use. Fit the tread over the old stair and apply pressure for 30 seconds. Finish by hammering in finishing nails 3/4-inch from each edge. Move on to the next stair, working your way up until you reach the top.