If a cleaning is all that it needs, try fine steel wool and mineral
spirits. I've used it on old furniture many times. If the finish is
totally worn through, you might be able to repair it, although that
takes skill and a bit of luck. If the wood is dirty, fine sanding and
app of matching stain....very chancy but "doable". I've mixed my own
stains using artist oils, linseed oil and min sp.

To clean it, vacuum thoroughly. If crud is down in the spaces between
boards, dig it out and vacuum again. Damp mop - don't leave standing
water on it - with tepid water and Murphy's Oil Soap. Sink protruding
nails. Use fine steel wool and mineral spirits, scrubbing with the
grain. Mop up the remains with clean rags or paper towels. Dispose of
the waste appropriately. A good, buffable REAL wax coating may be all
that it needs after that. They are nice and need only occ damp
mop/rebuff. Re-wax about once a year, depending on traffic and soiling.