Gary, you can turn on file sharing on both computers - you do have to designate what you are willing to share though in 9, (the easiest thing being the entire drive - using "Get Info->Sharing") and put things you want to share in OS X in your Public folder or your Sharing folder. If you look in the Apple Help menu it will give you a fair bit of info on the procedure (rather than me trying to describe it here and missing a vital step). Set everything up - adding yourself as a user in the Users and Groups panel in File Sharing in OS 9. Turn file sharing on for both computers and then you can use Go->connect to server in OS X, or Apple Menu->Network Browser in OS 9.
However, there are a couple of other options, which give you much more access to the files on your OS X computer - including using the URL of the other computer with "afp://192.168.0.xxx" in your browser - it will connect, ask you for your password - which on the OS 9 computer you've set in Users and Groups. If you are logging into the OS X computer from the OS 9 computer using this technique, simply use your administrative OS X password and voila - you'll have access to EVERYTHING on your OS X computer, not just the Shared or Public folders.
Between my OS X computers I use FTP (Transmit), since I have all the settings for both computers already set in the menu and it's fast. It takes me directly to the User folder - which is fine, since I'm not going to be messing around with applications etc. remotely. For some reason or other I can't get it to work with the OS 9 Mac - it refuses the connection, even though I've got the TCP/IP option checked in filesharing on OS 9. However, the afp:// method is equally effective, and gives you access to all drives, partitions and files (you just have to remember the IP addys for all your computers - which since you have only two on the network shouldn't be too hard...I've got 6 right now including 2 PC's and a print server with it's own IP, and I keep getting mixed up!!!)
Hope this helps...If I've left anything out, ask away! There are a lot of fiddly bits to filesharing...especially in OS 9 - leave one of them out and nothing happens.
Edit - my router uses 192.168.0.xxx - other routers use 192.168.1.xxx as the IP addresses handed out by DHCP. Check your IP's before you start!