You should have access to the library of the university that you are affiliated with for study abroad. If you haven't received a special orientation for the library, don't hesitate to ask for one. If you want to try using other university libraries, you will probably need a "letter of introduction" from either a professor or a librarian.
In most cases, you will be better off using a large public library or the National Library, which also function as research libraries. You will need to register to use the libraries (you must have your passport with you in most cases) and pay an annual fee and a deposit if you also want to check out books. Check the library's web page for more information on how to gain access.
In addition to public libraries, you might find private libraries are more to your taste. There is an article in CNN Travel about a private library in Shanghai called 2666, that combines good literature, coffee, and a cozy atmosphere.
It is standard operating procedure for many university libraries and archives to be closed to outsiders unless you bring a letter of introduction with you. Since the library/archive doesn't know you, they want some reassurance that your intentions are good and that you need to use the materials that they own.
You have a few options:
1. Have one of your Smith College professors write a letter of introduction for you.
2. Have one of your Chinese professors write a letter of introduction for you.
3. Have your library (either Smith or your university library in China) write a letter of introduction for you.
Have questions? email me email@example.com and I will try to help you figure out what to do.