Given the age, it's probably an 802.11b adapter, but for basic web browsing and such that's just fine. You should be able to just turn it on, and set the TCP/IP settings to get the information it needs automatically. It's been a good while since I've done much with any OS Classic version, that I can't reliably tell you how to do this from memory, and my iBook only has OS X on it.

The USB wifi adapter isn't likely to work with OS9 however. There might be a chance if you were running some version of OS X, but most OS Classic support dried up years ago.