The problem isn't SSH itself, but the tutorials out there tend to assume that you're using GNOME or KDE (or, more to the point, their automount systems). If you're not running either one, you're left trying to figure out how to deal with that problem.
Plug in the flash drive, then "tail -n 20 /var/log/syslog" (on most systems, and assumes the system isn't very busy), and look for the notification of the plug-in event with the device node, e.g. /dev/sdb1.
Then, "mount /dev/sdb1 /media/flashdrive", replacing the device node with whatever you see in syslog, and the mount point with the appropriate folder on your filesystem (really, whatever you want it to be -- you can mount something to your home folder if you like). 'mount' should be able to auto-detect the filesystem on the device unless you're running a really old Linux or BSD.
