You could use NFS:
For a Unix/Linux only system, NFS is probably easiest. Essentially, either system uses config files '/etc/smb.conf' or '/etc/exports' (server side) to describe what is being shared, and a server daemon to perform the actual sharing. The client side uses mount to make the shared directory visible on the client filesystem.
Have a look at the man pages, and give it a try. Come back here for more help with specific issues.