the reply above would only work if a /etc/fstab entry had automatically been generated for the zip drive. in general, you can mount a zip just like an ordinary hard disk, although you need to mout partition 4 for some reason.
try /dev/hdb4, /dev/hdc4, etc
mount -t msdos /dev/hdb4 /mnt/zipdrive (or whatever directory you want to mount it in)
once you've found the mount command which works, you might want to add an entry to /etc/fstab, something like this:
/dev/hdb1 /mnt/zipdrive msdos rw,user,noauto 0 0
then you could just do
as an ordinary user