If you were only interesting in being able to access the files, you might just want to look at NFS:
http://www.linuxdoc.org/HOWTO/NFS-HOWTO/index.html
But it sound like what you might also want is to be able to export an Xdisplay. Thats easy to do. Lets say you are on a box called "remote" and you want to run an X app on a box called "server". First... you have to give permission to "server" to display on "remote" so you issue:
xhost + server
Then, you telnet or ssh into server. From your remote shell, you issue:
export DISPLAY=remote:0
Then you just run an X application, in this case since you want to look through the file system, you might issue:
gmc &
and the Gnome Midnight COmmander will be running on "server" but displaying on "remote". Now.. than can get very confusing.. be careful.
Check out these for more info:
http://jgo.local.net/LinuxGuide/linux-X-remote.html
http://www.linuxdoc.org/HOWTO/mini/Remote-X-Apps-1.html
http://www.linuxdoc.org/HOWTO/mini/LBX.html
One other thing you might want to look into is 'Xnest'. There is info on
http://www.xfree86.org
That allows you to create and export entire desktops instead of just apps. I don't know a whole lot about it though.