Keep It Clean
Cleaning is a simple procedure if you do it after every time you play your string instrument. A simple wipe with a soft cloth to remove anything foreign, especially rosin and fingerprints, from the entire instrument—including the fingerboard and strings—is sufficient. If you do this before placing the violin back in its case and also clean the cloth itself regularly, hardly any maintenance on the finish will be required.
Keep It Polished (the Right Way)
As for polishing, I’m not enthusiastic at all about violin polishes, even the “good” ones. They contain solvents that work by lightly attacking foreign substances and eventually, the violin’s own varnish. They leave their own residues in the form of oils and waxes, which can attract dirt. If used excessively, they actually work their way into the wood and can frustrate future repairs (oil and wax reject glue) and cause tonal changes.
In addition to the daily cleanup, I prefer that owners simply use a damp (not wet) paper towel occasionally to remove skin acids and other water soluble substances from the instrument’s surface, followed by gently drying with a dry paper towel. This small amount of water does no harm if it is immediately removed. With a bit of additional gentle buffing with the same dry towel, you will achieve a pleasant shine that looks more natural than the one imparted by commercial polishes.