Hey there,
Well - as far as I know the two main options are NFS or Samba.
NFS is the main UNIX file sharing mechanism and runs over Sun's RPC service. Most Linux distros will have utils to help you set this up. If your's doesn't you can find *loads of FAQs and tutorials and HOW-TOs that can help you get this up and running. The points to be aware of with NFS is that some people consider it to be somewhat insecure (although this shouldn't be a problem if you've got your firewall set up correctly and only have the RPC service active on the intranet. I use it at home now and again and it works fine (was able to play MP3s served over NFS from my OS X box on my Linux machine, so now speed probs there

)
Samba is the Open Source implementation of the M$ SMB protocol which is used to share resources across a network. OS X is pretty well equiped to handle SMB file sharing - you just use the Finder to connect to the remote machine like:
smb://<machine name>/<share name>
(note that it *is* important to specify the share name - won't work if you don't)
you will then be prompted for credentials etc. and voila. sorted.
I've never actually set up a Samba server on Linux - but here again I've been told that there are some security "peculiarities" involved ... like the password being sent unencrypted over the network (has this changed??) ... but again, if you set up your firewall correctly it won't be a problem.
Of course you also then have the advantage that *should* you ever want to connect a Windoze box to your network (if you need a good laugh or whatever) then you will be able to connect to your file server sans problem.
There may be other options (I believe that SuSE Linux supports AppleTalk to some degree - whether it can act as an AppleTalk server I've no idea, though.) but these are the two I'm familiar with. So far, I've always used NFS on the server myself and the Samba client in OS X at work where we (unfortunately) have some Windoze servers

... but both have worked fine.
Hope that's of some help.
Cheers,
C