a) The driver has to support it
b) you have to enable it in your xorg.conf (Load glx, Composite enable plus your driver specific command)
c) you have to have OpenGL installed, if you want to use Compiz
With running X, check "xdpyinfo" - you should have at least "GLX" mentioned.
After that, you need a windowmanager with a compositor already included (Xfce's WM, Metacity of Gnome, kwm from KDE or Compiz) or xcompmgr has to be started.
The difference is mainly wether or not the compositor uses Xorg's Xrender/Xcomposite extension or requires OpenGL to render with GLX_texture_from_pixmap. AFAIK, xcompmgr and metacity and xfwm use only Xrender/Xcomposite; Compiz requires GLX_texture_from_pixmap/OpenGL support.
After that, you can use transparency and dropped shadows at least.
Grab xcompmgr (
http://cgit.freedesktop.org/xorg/app/) and drop some shadows for testing. (see xcompmgr --help)