Desktop environments are user specific configurations that determine the way a computer is run. The most common desktop environments are window managers that run on top of the X server. Some examples of these are KDE, GNOME, Fluxbox, XFCE, ect.
Desktop environments can also include command-line shells like bash, csh, zsh, ect. The only thing common among all desktop environments is that they are based on the users preference.
Most commonly, a desktop environment is chosen for you with the distribution that you picked. Ubuntu and Fedora defaults to Gnome. Mandriva defaults to KDE. Arch linux defaults to bash.
Common among all distributions are the locations in which the desktop environment can be configured. For all users, these are contained in the /etc folder. If you want to change settings on a per-user basis, then they are contained in hidden files or folders in the users home directory (always prefixed with a period).
To configure a graphical environment on the most basic level, the configuration file name is xinitrc. This tells the X server what it should do after its started. To configure a shell, the file is typically bashrc (or cshrc, ect). This will let you create shortcuts for commands, aliases, and set or change specific environment variables upon the execution of the shell. There are many configuration files that deal with this--but they are governed on a per-program basis. If a program executes on startup, or needs to execute on startup, then there almost always is a configuration file associated with it.
A failure to load a desktop environment can almost always be attributed to an improper setting in these hidden folders, and is often a first step in fixing a problem at bootup (troubleshooting usually begins at the log files).