New York City is served by three public library systems: The New York Public Library (NYPL), Brooklyn Public Library (BPL), and Queens Library (QL). Each system is separate—you need to get a different card to use each one in person or its online services—but all are free to anyone who lives, works, goes to school, or pays property taxes in New York State. You may apply for and get cards for all three systems.
Each library card/account typically allows you to use online databases from that Library's system, borrow books from any of the three systems (registering your account in advance may be required), and reserve books that are in one location to be sent to another location within that same system. See details on each library's site.
The NYPL has specialized research-only locations, as well as the many neighborhood libraries where most items can be borrowed. These library locations may be the most suited for FIT students and others looking for commonly-asked questions we get at the FIT Library.
FIT students and employees can get cards from each of the three systems. If you're not a New York State resident you can use your FIT ID as proof of eligibility along with government issued photo ID (like a drivers license or non-driver ID) from another state.
Check out the libraries' Culture Pass offers for free museum admissions!