All instruments should be cleaned regularly to keep them in good playing condition. For string instruments, the rosin from the bow lands on the instrument as dust. You can easily wipe it off with a soft, lint free cloth each time you finish playing. You can use an old, un-printed t-shirt, or a dishcloth. Don't forget to wipe the bow. It's best to use a different cloth for the neck, strings, and fingerboard, where you touch them with your fingers. Wipe the strings with the cloth and then pull it between the fingerboard and the strings. A cotton cloth can also be used for this, but some string players prefer to use a silk cloth. String instrument should always be stored in its case for safe keeping, and try not to expose it to extreme temperatures (eg. in a parked car during the summer or winter).
Other that cleaning cloths, there are relatively few supplies that you will need for your instrument. Here are a few suggestions available on Amazon or as an app: