The Command and Conquer Demo (approx 300mb) allows you to play the first two mission of the GDI campaign, as well as skirmishes on one map. There is also a brief tutorial mission to help introduce you to the game.
The demo is set to only allow you to play as GDI in the demo, but there is a way around that (see below).
To play as the Nod side on the C&C3 demo all you have to do is open up the skirmish menu, click on 'Nod' and then press 'N' afterwards; this will automatically change the menu to Nod.
You can also use this method to change the status of your enemy... e.g. to 'rusher' or 'guerilla' etc.
Be aware that you can select the Scrin as your side but the game won't work; it will simply come up with a 'You've been defeated' message.