You could use nfs to network the two machines. I havent used fedora before so I cant say exactly how you would install nfs but for debian you would install nfs-kernel-server for the server and install nfs-common for the clients.
Then from the server, you would edit the exports config file "/etc/exports" and enter in the path(s) for the folders you want to share.
For example, you could have the following in the exports file:
"/home/user/share *(rw,no_root_squash,async)
The "/home/user/share" is the directory you are wanting to share. The "*" means that any computer can access the share (you could replace this with an ip address. Then you place the options in. "rw" means read/write access which you could replace with "ro" (read only). I always put "no_root_squash" because this allows you to access the share as root, which is what I seem to do a lot (warning: this means that anyone logged on as root can access the share though!). "man exports" should explain more.
The other files to look at in the /etc folder are the hosts.allow and hosts.deny files. There should be comments in these files which explains how to use. You would use this files if you wanted to allow and deny certain ipaddresses from accessing the shares. Here you could put in hosts.allow "portmap: 192.168.0.0/255.255.255.0" which would make it more secure meaning that only ip addresses 192.168.0.1-254 can access the share.
Now, once your done with the server, you should be able to go to the client computer (make sure that you have installed nfs-common which should have started lockd and statd. Then you should just have to type "mount -t nfs ipaddress:share mountpoint"
For example:
"mount -t nfs 192.168.0.100:/home/jesse/share /mnt/share"
Hope that helps you.
I havent done nfs for a while so this is a brush up on me too. So there may be some extra steps that might have to be done...