1) With a feather duster, soft bristle brush or cotton cloth, dust all the surfaces of the wood furniture, this will help to remove the debris on its exterior.
2) Beneath the debris might be more stubborn stains like wax and grime, put a little mineral spirit (a solvent used for degreasing and cleaning equipment) on your cotton cloth , then wipe and rub it over the stained area.
3) For the corners and crevices, which can be rather hard to reach, use a toothbrush or soft-bristled brush. Put some mineral spirits on it, and brush the stained area. You can then wipe off the mineral spirits with a cloth after.
4) If your furniture came from a kitchen, there might be a stubborn layer of grease on it. In this case, try strong degreasers like TSP (trisodium phosphate), they come in boxes in powder form, you mix a specific amount in water, and apply and scrub it on the grimy area.
5) If the interior of your furniture has a strong odor, for example cigarette odours, you can get rid of the smell by putting bowls of activated charcoal or baking soda into the draws and other compartments. Leave it in there for a week, and the smell should be totally absorbed.