Polishing a violin doesn't change its sound, but it can make it appear nicer. Follow these steps to avoid damaging your instrument as you improve its appearance.
Determine if your violin needs polishing. If it's still new, chances are that it doesn't need it. Not only will it still look nice and shiny, but it will still have plenty of oils already in the wood. Polishing is best reserved for older violins, and only needs to be done occasionally.
Remove any accumulated dust from the instrument. Use a soft cloth, like an instrument cloth, which you can buy at any instrumental music store (it doesn't matter if isn't specifically a violin cloth, as long as it's soft). Be gentle and be careful not to damage or dislodge the bridge.
Apply a small amount of polish to a clean corner of the cloth. Consult the instructions on the polish as to how much to use, but as a general rule, be conservative. You want to avoid having access oil on your violin when you're finished.
Polish the violin using gentle, circular strokes until it is shiny and has absorbed the polish. Starting at the back of the violin when the cloth has the most polish on it will help keep the front from becoming too oily.
Avoid getting any oil on the strings of the violin. Oil on the strings or bow will keep them from being sticky and interfere with how the violin's playability.