This is going to be a challenge, but if you're up to it, it can be done.
1. You need to have either a USB 2.0 interface or 1394 interface on a controller card that works under 98SE. If the drivers for that are working properly, then an external hard drive should get recognized. This may require the latest patches/hotfixes from Microsoft as well. As was said above, the 1394 option is probably more reliable under 98SE.
2. The normal limit for drive size under Windows 98SE is 137GB/127GiB. This is because Windows 98SE only supports 28-bit LBA.
There is a guy over at the Microsoft Forum Network (MSFN) who has hacked the Win98SE disk driver stack and put in his own code to enable 48-bit LBA. Several people are using it with success. However, it's completely unsupported code, so who knows if it'll work on your system or not, or kill your data in some spectacular episode later on. 8O
If you want to try it, go
here and download the utility to check to see if your system BIOS supports 48-bit LBA. If it doesn't, then you're out of luck and the driver won't work anyway. Find a drive <137GB.
If it does, then go
here and download the Enable48bitLBA file for your system. Follow the author's instructions
exactly. There are several versions of the hacked driver file, you must download and use the exact one required for your build of Win98SE.
Note: You only need the hacked driver to use a >137GB drive. If your drive is smaller than that, you don't need it.
Be aware that you'll still have to format the drive as FAT32 even if you get the driver working, which will still limit you to the inherent limitations of the FAT32 file system (file size limit 4GB is the primary limit).