Clean the existing wooden stair treads thoroughly with a commercial wood cleaning product. Use a stripping compound to remove any adhesive from the stair treads.
Place a level on each stair tread. Use a floor leveler to make any uneven stair treads level. Floor leveling compound is available at many home improvement stores and flooring centers. Follow the instructions on the package when applying the leveling compound. Be prepared to work fast, as leveling compounds tend to have short curing times.
Measure from each side of the existing wooden stair tread to center the carpeted tread horizontally. Measure the distance from the tread to the next riser to center the carpet stair tread vertically. Peel the adhesive off the back of the carpet tread and press it into place. This is the procedure to use with the type of carpet stair treads that resemble small throw rugs.
Lay down carpet padding and staple it in place if you are using carpet pieces as stair treads. Make sure the padding covers the entire wooden stair tread.
Attach a tackless strip to the existing wooden stair tread. Pull the carpet tight around the front of the tread, then staple it underneath.