You will need the GGZ software on your system; it doesn't come with the Freeciv source code. Since it is rather new, it is quite possible that you have to install it from source. Go get
from http://ftp.ggzgamingzone.org/, or any newer, compatible version. They compile fine on Debian Sarge (in the order of below).
Next, you recompile Freeciv 2.1 Beta or any newer, compatible version of the Freeciv source code, like this:
./configure --with-ggz-client make make install
Note: As of Freeciv 2.1.2 the development version of the GGZ libraries are required. See the GGZ website for info on how to retrieve a copy of the source tree.
Now you're done. Start Freeciv as usual:
(or other GUI) You get a button Connect to Gaming Zone on the start screen. It opens a dialog with further details.
Note that the translation of the GGZ dialog within Freeciv isn't working yet, and that language support in general is weak, so you will most probably see it in English. As a workaround, you can start the GGZ with
This is only needed if you want to run your own GGZ server. You will need more libraries; please see the docs for this.