Run openbox or openbox-session with xinit. Note that only openbox-session provides autostart.
Note: After executing openbox-session, there is only a blank grey screen. Try to move your mouse and right click to get an openbox menu to make sure that it is actually working.
Other desktop environments
Note:
When replacing the native window manager of a desktop environment with Openbox, keep in mind that Openbox does not provide any compositing effects (such as transparency). See #Compositing effects.
Openbox does work with GNOME applications (but see GTK#Client-side decorations). [1]