Hi, Welcome to the group.
Provided your base station does not rely on an internet connection to provide addressing etc (i.e. the AE is operating as a DHCP server providing addresses, or you are using manually set addresses, or it is still connected to a modem/router acting as a DHCP server) computers should be able to talk to one another over the wireless network or, in your case, with one connected through one of the ethernet LAN connectors.
In your System Preferences > Sharing if you set File Sharing ON you should see (or you can set) your Computer Name by which that computer is accessed over the network. In the options button, select whether you want to use AFP or FTP to share files - you may have to turn AFP (the Apple File Protocol) on in the Network Preferences. Once sharing is set up, your computer should be visible in the other computers Finder under Network devices. If not, go to Finder > Go > Connect To Server... and ask to connect to afp://computername.local or
ftp://computername.local depending on the protocol selected.
I'm doing this referencing the 10.6 System Preferences, but from memory the same general approach applied in 10.3
Good Luck!