Depends a bit on which browser you are using and which browser version.
But for IE, you'll probably be looking at something along the following lines :
(1) Select File -> Import and Export.
(2)Select Export & click on "next."
(3)Select Favorites & click on "next."
(4) Choose a location your external drive as a backup directory
(5) Click on "finish" and your Favorites will be saved to disk.
Alternatively....backup your personal profile.
Login as another user with Administrator privileges and use robocopy to backup your profile to an external drive.