From the aging of the wood to the skills needed to make a string instrument, you can assume that any string instrument took years to complete. The making of string instruments perhaps involves the most craftsman-like skills of all instruments and they should be treated with utmost care.
Rosin dust that accumulates on the violin/viola needs to be wiped with a clean, cotton cloth after every session. This cloth can be kept with the instrument in the case. The bow should be loosened so that the hairs are just off the stick after playing. This can be adjusted with the screw at the frog of the bow. When playing, the bow needs to be re-tightened so that there is some tension in the hairs, but not so tight as to cause the stick to be straight or curved away from the hairs. Over-tightening can ruin or break a bow!
A cover for the instrument will help prevent damage to the instrument in the case from the bow coming loose from its holder. A pillow case works nicely for this, simply insert the instrument and tuck into the case.
Cleaning the instrument and bow stick should be done periodically with a special cleaner sold at violin shops. Never ever use a common household cleaner! Chemicals not designed for the fine varnish of the violin/viola can seriously and permanently damage the varnish. Store cleaners away from the instrument (don’t keep these bottles in the case.)
There are differing schools of thought on rosining the bow. What it boils down to is a matter of preference. Rosin the bow when the lack of it seems to be negatively affecting the sound (glassy sounding or generally slippery feeling.) It isn’t always necessary to rosin before every session—except with some bows that have synthetic hairs. Rosin with a gentle but firm motion, the whole length of the bow. Try to avoid the impulse to over rosin certain areas of the bow, it is better to have a consistently rosined bow.