In addition to the libraries housed by each Department, the central or main library is located in the so-called 'Henry Ford Bau' (C5 on your campus map.)
Since you are not allowed to take your bags and coat, be prepared to check those on the ground floor. If you walk upstairs, you can reach several areas where students can do online-research and access FU's Digital Library
. . .
. . . or study in designated spaces.
In general, computers in the library are reserved for research, so if you want to check email, you should do that in the Computerzentrum, located in the 'Silberlaube' (E6).
By using the online-catalogue, you have access to all the books available in all of the libraries. Just remember that every Institutsbibliothek has different opening hours and that the majority are 'Präsensbibliotheken,' meaning that you cannot check out books. Some do check out books over the weekend, but there is no general rule valid for all libraries except that they are all closed on weekends.
Since doing research here will therefore take considerably longer than you're used to, it's a good idea to define your research topic as soon as possible and start browsing the available catalogues early in the semester.
All images by courtesy of H.F.