Removing painted to expose wood grain requires significant effort. How much effort depends on the type of wood, the type of paint, and how much paint has been applied.
The simplest approach is sanding. If the wood is thick and you have access to a professional sanding machine, this can be done, but this process generates a great deal of dust that needs to be collected, and, if the paint is old, presents a lead hazard. Mask, vacuuming and heavy duty filters are required.
Chemical stripping avoids most of the airborn dust (and lead) and can remove the bulk of the finish. A follow-up sanding is needed. There are several new citrus based strippers that are fairly effective and avoid the more toxic chemicals of the solvent based strippers.
If the wood is open grained (like oak) it is likely that paint will remain in the grain, necessitating a deeper final sanding.
If the floor is very small, hand scraping is possible, but again, masks and vacuuming are essential and again, a final sanding is necessary to get it ready for finish coats.
Sanding of floors is almost always done with larger commercial type units, using ever finer grades of sandpaper. If the area is small and you are patient, a hand-held belt sander, or even an orbital sander may work.
Best Answer
You can actually just use an eraser as long as you use it gently. Even a simple pencil eraser can handle the problem, but you can use art gum erasers or suede stones as well. If you want to go a little further, baking soda or toothpaste dabbed onto the end of a soft cloth has also been known to work.