ZIP drives come with many different types of interfaces. The most prevalent were:
- Internal ATAPI version, most commonly installed in PCs. (An IDE version also existed, but was rather uncommon.)
- External Parallel port version, most commonly connected to PCs.
- Internal SCSI version, most commonly installed in early Macs.
- External SCSI version, most commonly connected to Macs, or other computers that commonly had DB-25 external SCSI ports (i.e. Amiga).
So, the first thing you need to determine is which version you have. Actually, it's not so easy to visually distinguish the external SCSI from the external parallel port version. ZIP also made an external drive that supported both of these.
Assuming you have an external drive, it's not a trivial matter to use it today. You are unlikely to find a modern computer with an external SCSI port. Some modern PCs do have the old Parallel Port, but it will need to be specifically configured for the ZIP and you will need the Driver that was designed to use it. Which means you will need to be running the OS that supported that driver - probably an old versions of Windows 9x.
The only ZIP drives that are easily supported with a modern computer is the internal ATAPI version, simply because you can attach it to a modern USB<->IDE converter and use it from a USB port. Then, the only issue is having an OS that supports whatever filesystem is present on your ZIP disks.
The internal IDE version might also work. The difference between those versions is that the IDE version didn't require any drivers, it worked just like a hard disk. Obviously changing media didn't work so well since the software might not recognize the change. The ATAPI version worked with a driver, similar to CD-ROM-drives. Later BIOS releases often offered an option to boot from an ATAPI drive, and later Windows versions also supported these natively.
More specific answers will require a better description of what you have:
- Which version of ZIP drive hardware?
- Which filesystem is used on the ZIP disks?
- What kind of computer/OS do you have that may support the right interface or be able to use some USB converter?
- Are you willing to setup a special computer, or at least a virtual machine, to try to read your ZIP disks?