You can definitely network OS 9 and OS X Macs. I don't have an AEBS, but I think it has a LAN port (for a wired connection). So you need the following setup:
cable modem--->WAN port of AEBS--->wireless to PowerBook
LAN port of AEBS--->G3 Mac
After you get all the network settings configured according to yourarticle, then turn on file sharing on the OS 9 Mac, and share whatever folders you choose (you can assign a password if you like). This is done in the "Users and Groups" settings when you do "Get Info" (Cmd-I) on a folder.
Then on your PowerBook, use "Connect to Server" (Cmd-K), and type in afp://xxx.xxx.xxx.xxx (where the Xs represent the IP address of your G3). Enter your password, if assigned, and away you go
Edit: If you need more info on configuring your network settings, the AEBS user manual should have a good description, or just post back here.