You say dirty and dusty, if dust try some Dri Tack cloths, the tacky cheesecloth you use after sanding. I dirt embedded in the grain, try some Murphy's Oil Soap before trying light sanding, which is a last resort thing. Apply as sparingly as possible, with as little water as possible using a lint free cloth dampened with a diluted mix. Contrary to popular opinion, a little bit of moisture will not immediately warp wood. However neither do you want to soak it down with gallons or water. Rinse with a little bit (again, little bit) of clean water and dry immediately with lint free cloths. If stained with some residue that Murphy's or light sanding won't fix, you may need to bleach the wood. Sanding and bleaching are last resort options when you have nothing else to lose.
