Please be careful with the CompizConfig Settings Manager tool. Choosing the wrong checkboxes could result in an unresponsive Unity Desktop. I've done this myself and the only way out is to use dconf to reset the desktop to defaults or just do a complete reinstall. This is not fun.. You have been warned!
First off, make sure CompizConfig Settings Manager is installed. This can be installed via Ubuntu's Software Center.
After CompizConfig is installed, launch it. In the main window, uncheck Animations and Fading Windows. Be sure to wait for the desktop to catch up. Sometimes, Unity pauses and flickers (maybe it's a Unity restart).
After that, click the Window Decoration button (don't uncheck that one). Expand both the Active Shadow and Inactive Shadow boxes. Reduce in both areas, Shadow Radius to the lowest value 0.1000 and Shadow Opacity to 0.0100. In addition, set the Shadow Offset X and Y to 0. This reduces the need for compositing the shadow over other objects.
So far, these minor adjustments have brought a few slow machines back from the grave. Hope this info helps and if anyone has anything to add that could speed up older hardware, I'm all ears.