Dirt can be removed from bare or finished wood using a suitable solvent. White spirit or turpentine will dissolve grease and grime; warm soapy water will remove any water-soluble dirt.
Initially use a natural fibre (e.g. cotton) cloth wetted with the fluid. If a more aggressive cleaning action is required, use the fluid in conjunction with steel wire wool (the coarsest grade which does not cause visible scratches; try grade 00 or 0 first). Caution! This method is not suitable for cleaning gilded articles or those with finely painted decorative effects. Delicate use of cotton swabs is more appropriate in these cases.
Bulk solids which are softer than the substrate (the wooden surface or its finish), are best removed using steel scrapers. The sharpness of scrapers should be carefully controlled so they easily penetrate what you wish to remove, but not the substrate.
Bulk solids which are harder than the substrate must be cut away using sharp-edged tools like chisels. Thin layers of hard residues can be removed using convex-curve-edged knives, without penetrating the substrate. Sharper edges give better control and sensitivity.
If the dirt is sealed below layers of finish such as varnish or French polish, the finish must be removed first. If the finish is in poor condition this may be done by abrasion. Sound finishes are more economically removed by chemical paint strippers but beware that some types can damage the wood structure. Follow the manufacturer's instructions carefully.
Allow the wood to dry thoroughly before applying other finishing treatments.