What Can I Do to Take Care of My Strings?
1. Purchase quality strings. Just like tires, air filters, and shoes, there are strings that are made well and ones that aren't. When it comes to instruments, at least, much that is dirt cheap is more likely made for a quick buck than a satisfying (or even functional) customer experience. Talk with your teacher or local violin shops about what strings have the best quality.
2. Avoid extreme temperatures. There are all kinds of forces at work on an acoustic instrument at any given time. Do yourself a favor and keep your instrument at room temperature. Never leave it in the car and don't store it next to a radiator or air conditioning vent. This will prevent many problems with the whole instrument!
3. Wipe off your strings during every practice break. All strings are a core material wrapped in some type of metal (usually aluminum, silver, or gold). Over time, the acidity in your sweat begins to break down the winding on the string. Use tissue paper or a cotton rag to wipe the strings and minimize this effect.
4. Go back to your local violin shop and talk with them if you had a bad string in the set that you purchased. Occasionally, bad strings make it into a set. You can know this if the string unravels within the first month of use. Any other type of early breakage is usually due to tuning.
5. Don't exert too much pressure. This takes time to learn. However, it is important to do all of the work that your private teacher tells you to do. Your bad technique can harm your joints, performance, and instrument. If you take the time to learn how to relax, it can keep strings from going out sooner.
6. Check with a luthier if they break frequently. Providing that you purchase quality strings, they don't typically break within a short period of time (UNLESS they are tuned wrongly). Talk to an experienced luthier about possible structural problems with the instrument and get any necessary repairs.
7. Be careful when tuning. Don't turn a peg too quickly. Make sure you are hearing the pitch and don't tune the string too high. These types of tuning errors often lead to strings breaking.
For an intro to some quality string brands, read a previous post called "What Brand of Violin String Should I Purchase?"