Non-techy, simple instructions:
1) Plug n Play: If you're using a PC, on Windows 2000 or better, likely the external drive will be automatically "recognized" and installed as soon as you plug it in. Or if you have, supply drivers from CD/DVD that came with it. If not, download drivers from the web when installation asks for drivers.
2) Without software: You can backup files directly by dragging files, or copy-paste files to your ZIP drive. Due to the small size of ZIP disks, they're designed to backup only critical files and not your whole drive.
3) With software: Alternatively, ZIP drives also can use backup software (which you're likely missing unless your PC is unchanged since you last used the ZIP drive). That software allows you to tag your critical files so you can routinely or automatically back it up (as long as your external drive is attached).
Iomega, the manufacturer of ZIP drives, also gives walk thru's on their website. Here is a launch page for their support files, drivers, and software if you lost yours:
https://iomega-na-en.custhelp.com/cgi-bin/iomega_na_en.cfg/php/enduser/cci/product.php
(END of non-techy, simple instructions.)
Please note: An external ZIP drive is a magnetic tape backup drive and also known as is removable storage. I believe this is what you have and not an external hard drive.
Extra: You have to consider at least a couple of other things using external backup. Even though it's external, if your room burns down, so does that external backup drive.
Backing up to DVDs only goes so far because depending on conditions (temperature, etc) the image surface degrades and you have to re-back them up again after a few years. Magnetic storage was more viable on the shelf longterm and that's why many business used to use magnetic tapes.
I gave up on ZIP disks because they're expensive. The cost of replacement ZIP drives exceeds many other options. You may consider other devices available today (external hard drives, flash drives, etc). Up to you based on cost and convenience.