Download #2 on this page.
Get that .sit file to the eMac's hard drive, you may need to drag it to the hard drive instead of the desktop.... Mac OS handles stuff on the desktop weird when multiple drives are involved, I won't overload you with the details right now... Anyway, if that .sit file shows up with a c-clamp or other colour icon you can try double-clicking it. If it asks what you want to open it with, select Stuffit Expander. If it has a white generic icon you can try dragging it to Stuffit Expander... Possibly in an Internet Utilities folder, but I can't recall off the top of my head. Either way it should decompress to a .img file, this is a disk image. Commonly Stuffit automatically mounts those onto the desktop with your other disks, but if it doesn't just double click the .img file and "emac-ati-drivers" should show up on your desktop, and double click that to open it. That should open to the folder full of stuff you need.
I know this all sounds rather convoluted, it'll seem less weird when you are more familiar with the processes involved here and why things are being done this way.
If you have troubles such at the system freezing while booting, you can hold the Shift key while booting and Mac OS will boot with extensions disabled. This will allow you to do some clean-up if needed.
About the Desktop business: each drive has a hidden folder on it which contains items that are displayed on the desktop. Of course if you only have a single drive and locked/non-writable media that's all well and good, but with multiple writable drives one might lose track of what files are actually on what drive. We just want to make sure the files you are working with here always reside on a HFS or HFS+ partition and I can't remember how Mac OS 9 will be handling this particular situation if you are using a FAT formatted USB drive or what, it's been a long time since I did that. Not sure what format you are even using in the first place, which is why it's just simpler to start by copying what you need to the hard drive. Other filesystems don't properly support the way Mac OS stores it's data and things get broken, this is why we use .sit instead of .zip. You'll learn about this in due time, but lets just get you running first if possible.
Hopefully I've remembered everything correctly, someone will probably chime in if I'm wrong.