Furniture, Wood and Cabinetry Finishing - maple furniture

I want to clean a 50 year old dresser and bed; they are both solid maple. They have no varnish or poly. covering the stain that is on them. The dresser has dirty marks (a darkening) around the drawer pulls and the bed has the same on the tall posters from hands touching them over the years. How do I begin to clean these items so not to damage the wood? After cleaning I would need to see if they required refinishing or new stain. Any advise would be greatly appreciated.

Mousie:

You can use what I normally use in my shop to clean furniture - VM&P (Varnish & Paint Makers) Naphtha. It's available at paint stres and home centers.

It's better than paint thinner (mineral spirits) in that it dries faster and leaves no residue. It is highly flammable, however, so take proper precautions. Use with 0000 steel wool and rags.

I sure appreciate the info and I am going to head up to Lowes and get the product and get to work! Thank you very much