If there is already old carpeting installed on the stairs then the first step is to remove it. This can be done by prying it up at the corners of each step using pliers. You may also have to use a carpet knife to make incisions into the material in order to create hand holds to grip at it. In either case work carefully so that you do not damage the wood of the stair below.
Once the carpet and the padding beneath it are gone, inspect the tackless strips and see if they still have their hooks in place. It may be possible to reuse them for the new carpet installation. If not they should be removed using a crowbar, and or a chisel. Pliers can be used to pull out staples and nails that secured the previous carpet in place.