To access the Boston Public Library's online resources, including JSTOR, you need a BPL card. You don't have to take a trip to Boston to get one, though - you can register online for an eCard. If you're signing up for the first time, need a new eCard number, or need a refresher on accessing and using JSTOR, check out the BPL eCard and JSTOR Tutorial under Tutorials and Tips in the tabs.
JSTOR is one of many databases you can access with a BPL eCard. Take a look at the full list, or add the BPL as one of your libraries in OverDrive.