Hi Glenna, What is the material?
Glenna...You can always sand then paint, use napkins, etc. and mod podge or contact paper will work. Good luck!
If you have furniture that has a faux wood grain plastic veneer, there is really no easy way to fix it. You could try sanding the area smooth, coating with a bonding primer, and then trying to repaint the area in a wood grain color and pattern to match. You could also try covering the entire surface with a thin piece of plywood and stain it to match. The most extreme fix would be to re-veneer the whole surface.
I have the same problem on my old computer desk. I was thinking of painting it black to cover/hide the worn areas. Figured this was easiest way to go. I already have the black paint so it wont cost me anything. black hides everything and will go with the neutral décor of the bedroom. The computer is gone now but I still use it as a desk and now that the desk top is exposed with the computer being gone I need to touch the worn areas up. Id say to paint it and if you don't like the way it comes out then cover it with contact paper.