Assuming that you are using the stock kernel that came with your install this procedure is quite easy. If you have recompiled and not included scsi support, scsi disk support, and Iomega zip as a module you need to do this before you can use a zip under linux.
First off make a directory to mount your zip in. I like /mnt/zip. Now as root type insmod ppa . Next type insmod lp . Assuming you are using a pre formatted dos zip disk you need to to mount it. So type mount -t vfat /dev/sda4 /mnt/zip . That's it you can use it just like any other disk. You can format for the ext2 filesystem as well with fdisk just like any other disk.
The last thing I recommend is you use put an entry into /etc/fstab so that you do not have to type mount -t vfat /dev/sda4 /mnt/zip all the time. I prefer to use linuxconf to do this and just add it as a file system, also making it user mountable.