Running

You can either start gnome-shell "nested" in a window within your current 
session, or you can run it within your session replacing gnome-panel and 
window manager.

Depending on the state of your X drivers, one or of the other of these may
work better. So, if the first one you try doesn't work, try the other.

====

Running gnome-shell replacing the panel

This approach is best when trying out the GNOME Shell and wanting to see its
full potential.

gnome-shell --replace

When gnome-shell exits (you can kill it with Control-C in the terminal in which
you started it), gnome-panel and metacity are restarted.

====

Running gnome-shell nested

This approach is useful when developing the GNOME Shell and wanting to quickly
test some changes. NOTE: It isn't useful for getting a good feel for how the
shell works since it will be really slow, and won't properly integrate with
the rest of your desktop.

gnome-shell
(This requires a relatively recent version of Xephyr with GLX support to be
installed on your system (x11-servers/xephyr).