On Windows: External drives show up as additional drive letters and can be selected like local drives.
On Mac OS X: In the Backup tab, enable the Show Hidden Files control. When this is enabled, you'll be able to go to the very top (root level) of the file system and see /Volumes. External hard drives will be available for selection from there.
On Linux: External drives show up on the directory tree where they are mounted in the filesystem, typically under /run/media.
If the external drive does not appear immediately, please wait a few moments, or close and reopen SpiderOak. When the program reopens, the external drive should appear.