How Should I Store Brown Sugar?
I always store brown sugar in an airtight, ziplock bag. That works pretty well for preventing it from getting hard. It does not need to be refrigerated. 

However, if your brown sugar is already hard, there are a few techniques that people often recommend for resoftening it. These include: storing it in a closed container for a short period of time with apple slices (which will impart moisture); doing the same with a slice of bread (which will also impart some moisture); or, briefly microwaving it. 

Here is a cooking blog which discusses some of these approaches: 
https://www.thekitchn.com/4-ways-to-soften-brown-sugar-and-keep-it-that-way-195922