Note: If you are using the legacy AnyConnect application, you must upgrade to Cisco Secure Client (learn more here).
You rarely need to connect to the VPN to access library resources. Generally, using the links on the library's website (such as the databases page) will authenticate you as needed and provide you access regardless of your location.
However, if you do need to use the VPN, here's how:
Mac OS users must enable “Cisco Secure Client - Anyconnect VPN Service” in your system settings (System Settings > General > Login Items > toggle to enable "Cisco Secure Client - Anyconnect VPN Service" (see step-by-step instructions here).
Open the Cisco Secure Client application.
Connect to su-vpn.stanford.edu (you might need to enter it or select it from a drop-down menu).
In the Group drop-down menu, select either the Full Traffic non-split-tunnel or Cardinal Key Full Traffic option.
Enter your SUNet ID and password. Press OK. Use one of the options to multi-factor authenticate.