Before using polish on your piano, be sure it is actually necessary and beneficial. In general, most manufacturers recommend using against polishes because of the potential for damage to the finish and contamination of other parts of the instrument.
Common household products such as "lemon oil" or inexpensive "furniture polish" should be avoided. Despite the labels' claims that they "protect" the finish or "feed" the wood, they offer no protection from scratching and can actually soften the finish if over-used. Worse, they often contain silicones and oils that contaminate the wood, complicating future refinishing or repairs. Silicone is especially dangerous because of its tendency to spread within the piano, sometimes causing extensive internal damage. Avoid aerosol products altogether since the over-spray can contaminate piano strings, tuning pins, and action parts.
An appropriate polish can help to restore luster to a dulled finish or reduce the tendency of some finishes to show fingerprints. However, it should be applied sparingly and infrequently, and all excess should be wiped clean with a soft dry cloth so no visible film remains. To prevent scratching, always dust before polishing. Specific recommendations follow.