The easiest but most expensive option is to buy renovation steps available at better hardware stores. You just lay them over and glue them down (of course, you have to cut them to size). But expensive, as mentioned.
A budget version I have done is to take regular laminate flooring (click flooring) and glue it onto the steps. Then, of course, you need some stair nosing; in my case, it was regular edge moldings (see image). You may also need to supplement with some quarter round at the back edge, for example.
However, if you have unlimited time and patience, get a good detail sander and sand the entire staircase down to bare wood. But I disclaim all responsibility, for there are more than a few who have ultimately broken down into paroxysms of tears and had to be led away screaming after attempting such projects. The glue may let go now, but when you have to scrape off the remains... oh dear.
[image]
Look how nice with laminate flooring of the same kind as on the floor in the hallway.