If you have a very small child, you may not want them to have access to a full-blown desktop. It is possible (and pretty easy!) to set up a special X session just for your very small child that will let them use only one program. The two educational suites gcompris and Childsplay are perfect for this as they provide a number of different activities within the one program.
Below is an example of how to setup a special X session so that when the child clicks on their picture at the login screen (gdm here) they will be automatically logged in and run gcompris. When they are done, and exit gcompris, their session will end and they will be logged out.
figure out which package you want your very small child to use as their X session. gcompris or Childsplay are ideal for this. Determine the executable binary to launch for this (for gcompris it is /usr/games/gcompris).
build a .desktop file for the session. It should be located in /usr/share/xsessions. The .desktop file tells the session manager (gdm here) how to launch the user's X session. here is an example:
[Desktop Entry] Encoding=UTF-8 # The names/descriptions should really be better Name=gcompris Comment=This is the gcompris educational suite Exec=/usr/games/gcompris Icon=/usr/share/pixmaps/gcompris.png Type=Application
Change the user's ~/.dmrc to point to this .desktop file. The ~/.dmrc file tells gdm which type of session to launch. gdm takes the value of the Session variable, tacks a .desktop on the end, locates that .desktop file and launches the session according to its contents.
Be sure to set up the child's user account with no password passwd -d <child's login> and setup gdm with a browser configuration so the child can just click his or her way in. Setting the HappyGNOME theme with browser in gdmsetup is good for this.
Finally, put an appropriate picture in the child's ~/.face file. The easiest way to do this, in GNOME, is through Desktop --> Preferences --> Login Photo.