From our Borrowing pages:

UC Extension students, including those concurrently enrolled in UC Berkeley may purchase a six-month Library card by presenting proof of current registration. The fee is $25. All applicants must provide proof of California residence by presenting a current government-issued ID such as a driver's license or passport. Payment may be made by VISA, MasterCard, American Express, Discover Card, bank debit card, personal check or money order, made payable to The Regents of the University of California.

One-year and six-month Library cards grant borrowing privileges and access to the Gardner (MAIN) Stacks, Moffitt Library, and most subject specialty libraries, however, privileges do not extend to Interlibrary borrowing services, or access to course reserves. Access to special collections and services may be restricted. Cardholders may have a maximum of twenty books checked out at any given time. Note: UC Extension students who are concurrently enrolled in UC Berkeley are accorded the same privileges as UC Berkeley students.

If you have questions, contact the Privileges Desk in Doe Library, Floor 1 at 510-642-3403 or privdesk@library.berkeley.edu.