With Zip drives, a disk should never be inserted until after the drive is powered up. And the disk should always be ejected prior to powering down the drive. Leaving a disk in the drive while powering it off/on can be bad for both the drive and the disk. It seems that Zip drives are like older hard drives in that they don't park their heads automatically when powering down. If you accidentally turn a Zip drive off with a disk in it, it would probably be best to use the emergency disk eject hole to remove the disk before turning the drive on again. However, if you have an ATAPI drive, this is a real nuisance as you would have to open up the computer case to access the eject hole. In my opinion, this probably isn't worth the trouble (I think the newer ATAPI drives may park their heads when shutting down Windows - even without the IomegaWare installed), but I would still recommend that you try to avoid leaving a disk in the drive when powering down.
With Jaz drives, you should wait until the drive is powered up before inserting a disk. But once the disk is inserted, it's OK to leave it in the drive when you later turn it off/on. In fact, I recommend that a Jaz disk be left in the drive until you need to use another Jaz disk or until you need to move the disk and/or the drive. Ejecting the disk at other times will just cause unnecessary wear and tear on the load/eject mechanism, and it will create more opportunities for contaminants to enter the drive or disk. However, if you know that you won't be using the drive for an extended period, then it might be best to eject the disk and put it away. Otherwise, if you continue to use the computer, the drive would probably be subjected to a number of unnecessary spin-up/spin-down cycles.
Never move a Zip or Jaz drive with a disk inside (regardless of whether it's powered up or not).
Zip and Jaz disks come already formatted, and there should rarely be any reason to format them yourself unless you're using an operating system other than the one for which your disk was formatted. When formatting the disks, it's best to use the Iomega software due to the proprietary features of the disks. Formatting with other software can be risky, so avoid it unless you're sure you know what you're doing. Also, avoid using the Long Format option unless you want to use it to test a new drive or unless you're having problems with a particular disk. It seems that some drives work perfectly well in ordinary use although they may have difficulty with long formats, so long formatting when everything seems to be working well may just be asking for trouble (at least if your drive is no longer under warranty).
Both Zip and Jaz drives use a proprietary method of handling bad sectors automatically as they are encountered. Do not use non-Iomega software such as Norton Disk Doctor or ScanDisk (in Thorough mode) to do surface scans on Zip or Jaz disks. If these programs attempt to fix any errors they find during a surface scan, they can interfere with the drive's handling of bad sectors; this can reportedly render a disk unusable.
If you want to test a drive or disk, you can use the Long Format option of the Iomega software. If that completes successfully, the drive and disk are probably OK. This will, however, erase any data on the disk, and if the format fails (try several times before giving up), the disk will be unusable until it can be successfully long formatted. Non-destructive testing can be done with Steve Gibson's TIP utility (which also contains lots of good information).
It's good practice to give each of your removable disks a unique name (aka label or volume name); this can help to avoid problems when changing disks. If the OS doesn't recognize that you've changed disks, then it's possible for the FAT of the first disk to get written onto the second disk (which is not a good thing for the second disk).
In Windows 9x, right-click on the drive's icon in My Computer or Explorer, and select Properties from the pop-up menu. Here, on the General tab, you should see a Label box where you can enter a name for your disk.
Do not simply place all your files in the disk's root directory. The root directory allows for a limited number of entries, and you're likely to run out of those before you fill up the disk. Create one or more subdirectories (aka folders), and store your files in them. See this Microsoft Knowledge Base article if you want a detailed explanation.