Using steel wood to polish wood might seem out of place and actually harmful to the surface of the wood, but it isn't if done properly. The steel wool is very fine and will actually scrape off a very fine layer, leaving a silky smooth finish often referred to as a hand rubbed finish. The process is usually used on higher end pieces of furniture as the time involved increases the cost.
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Using a new (0000 or 4/0)) wool pad, apply some wood wax to the pad. Apply in curcular motion, going against the grain with just enough wax to coat the surface lightly. Rub thoroughly working it into hard to reach areas until the surface feels satiny smooth and not slick.
Allow the wax to set up for a few minutes, and then buff with a soft dry cloth. On uneven surfaces a furniture brush may have to be used to get into all the nooks and crannies. Work in circular motions.
Apply a second layer of wax, this time on a soft clean cloth, rubbing in circular motions until the surface is covered lightly with the wood wax. Allow this to set up for an hour and buff as before using a soft clean cloth.
Apply a third layer in the same manner as the second, only this time allow it to set overnight. Buff in the morning to a fine luster. Three coats of wax is usually enough for a beautiful finish.