Probably the most disorienting thing to a *nix newbie is the fact that, unlike Windows, where the GUI is an integral part of the operating system, *nix GUIs are completely optional. It is common for *nix servers to not use GUIs in order to free up valuable resources for what really matters: serving users. Another big difference between Windows and *nix is that you have a choice in windowing systems. You can choose between Xorg or XFree86 for the infrastructure and between any number of Windows Managers that actually control the appearence of the desktop (KDE and GNOME being the most popular for desktop computers). Installing a windows manager is nontrivial. You should probably start with Installing Software with Yum.
If you find an entry named X11 then surely you have a windowing system installed. As X11 is the directory holding the X configuration files.
Linux as other *nix have run levels. Somewhat like Windows safe mode and normal mode and command line only mode. There are 6 runlevels in Linux. If I recall well Fedora uses level 5 for GUI and all systems up. I think runlevel 3 all systems up, but no network. 6 is reboot 0 is shutdown 1 is safe mode single user and I don't recall if 2 and 4 are used. So another reason you might not be getting a graphic system is that you're on the wrong runlevel. Remember that as mentioned before a pure text based runlevel is perfectly fine in the Linux world. So you might have hit something in the setup that defaults you to a text only runlevel (say 3 in Fedora).
There is a file called inittab in the etc directory (/etc/inittab) that will tell you more about your runlevels and which is the default.
I my case a Kbuntu I run 2 as my default. If you find something other than 5 in your Fedora change it to five and reboot. See what happens.
As extra knowledge. Once you know you default runlevel look for directories in your /etc directory that look like rc0.d, rc1.d, rc2.d, etc (no pun intended). The number after the rc means the runlevel in which the the contents of such directory will be executed. For example if I enter runlevel 2 ( by os settings or typing telinit 2) all the scripts in the rc2.d directory will be run.
For example this is the content of my rc2.d directory:
Notice the S##Name files being links (if you don't know what a link is type "man ln" on your shell) to other files. It tells Linux to Start all those services by runing those scripts in START mode. If it had K##Name it would mean KILL that process. Just check out your rc6.d directory and count the Ks. Remember runlevel 6 is reboot!
In my case the rc2.d contains>
Which starts the graphic windowing system. As the following sniplet from the file shows "less /etc/init.d/kdm">
As a side note graphic windowing system isn't a redundant term. Just ask those who remember DOS text based windowing systems.
Anyway getting back on track. Not only does X have to be installed it needs to be configured to startup via a link in those rc#.d directories. You have to be in the runlevel that actually starts it! And of course you had to have installed a window manager (KDE, Gnome, etc). Or otherwise you'll only get the X window view which isn't a whole lot of fun.
Fedora comes with the X Window system and at least 2 desktop manager systems (Gnome and KDE). Gnome is the default. Other desktop managers can be installed and activated as well.
For a server, however, I don't recommend a windowing system at all. It will suck up at least 60MB of RAM and 98% of the users - which is to say everyone who talks to the server except for sysadmins - won't see any benefit worth mentioning (it can be tapped if you're generating graphics on web pages, but even there a GUI isn't essential).
One of my servers is an old P200 with only 98MB of RAM on it. To run that using a Gnome desktop would probably make it catch fire and burn to the ground. So I don't run X on it.
Whether or not X and a desktop manager (and GUI apps) get installed depends on which options you picked when you configured the server. Linux is very flexible that way.
"privilege" comes from the Latin words for "private" and "law" (legal) and dates to feudal times. To "claim privilege" meant that you were above the laws that applied to the common people.