Keeping your instrument and bow in shape so you can sound your best
Here are some things you can do:
Consider insuring your instrument through a home owners policy to cover fire, theft, and/or damage anywhere the instrument goes. *Most insurance companies Do Not cover the cost of theft or damage to an instrument left unattended in a car.
Don't store near a heater, near an air-conditioner, or in a car by itself; basically don't leave your instrument somewhere you wouldn't want to hang out. A trunk of a car is not a good place to store an instrument, as the trunk is not regulated.
Always store your instrument at a humidity of at least 30-40%. Use a humidifier and or dampits in the wintertime.
After playing, wipe excess rosin off of strings and instrument top with a clean, dry cloth. Wipe down places that you come in contact with as a player, too: pegs, chinrest, neck of instrument, upper bout of body. Carefully wipe the frog end of the bow, watching out for stray bits of wood from possible fractures. Regularly wiping down your instrument and bow can help stop the spread of germs. I love a clean, white microfibre cloth. It's really easy to see when it gets dirty - so you know you need to wash it. Also, please wash your hands before playing your instrument. Do not share your instrument with other people who might have a cold. I don't feel like I should have to say some of this, but it is not clear to everyone.
Use "Hill Peg Compound" to alleviate sticky pegs. If they slip, it's ok to put a little chalk on the peg, but use sparingly. Also, check that the strings are wound around the peg properly - this will help.
Keep bridge upright and lubricate the string grooves with pencil lead. If the bridge starts to lean too far, it will fall down. Video below on how to straighten a leaning bridge.
When installing/adjusting your chinrest, never over-tighten. This can lead to rib cracks.
Replace violin/viola strings once a year, once every 2 years for cellists. This is a rough estimate and just a starting point based on my experience of how long strings can last with moderate playing. Dirt/rosin and playing time/style can shorten this estimate greatly. Replace the strings one at a time, as the tension of the strings across the bridge is the only thing holding it to the instrument. The bridge will fall off if all the strings are taken off at once. Also, if your soundpost is too short, the post is likely to fall over inside the instrument if there is no string tension across the top.
This is specific for fine tuners for violin/viola: avoid the long arm fine tuner, as it changes the physics of the system for the high string and the ideal contact point for the bow on the string will shift towards the fingerboard only for the string with the long arm tuner. A durhill style fine tuner is much better, or for many beginner and intermediate players, a Wittner style tailpiece is great as it has all the fine tuners.
Cellists: be ever aware of the endpin. Especially if the cello is unattended and other people are around. An unseen endpin is easy to trip over.
Always loosen bow hair after playing to prevent the stick from warping or losing camber.
Take special care with the fragile tip of your bow. Inspect the ivory regularly for cracks. If an ivory chunk is broken off, put it in a safe place and have a professional fix it ASAP. The ivory tip protects the fragile wood of the head of the bow and the wood will wear or break over time.
Consult a professional for the following:
Open seams (when the top or back separates from the ribs - this is expected to happen otherwise the wood might crack.) This will happen especially during seasonal changes.
Cracks should be addressed ASAP to prevent them from expanding and getting dirt in them. Do not touch the crack. It will be much more difficult to clean, glue, and make disappear if it has even a tiny amount of finger grease, or missing/rounded over wood/varnish.
Soundpost adjustments: Have the soundpost checked at least once a year. It is common for newer instruments to need a new one installed after a year or two, as the body of the instrument goes through some initial stretching.
Also have bridge checked for warping and to make sure it has not moved out of position (the bridge is NOT glued down.)
Fingerboards have to be planed every 1-2 years depending on how much you play.
If you experience pain in your fingers/hands/wrist/neck, ask if there are any adjustments to the set-up that might help; ie string heights, getting a new soundpost, trying a different chinrest.
Active players should get their bows rehaired at least once a year (again depending on how much you play.)