All three of the above posts have many good and interesting things to say about Shock and Awe, but none of perform the important task of actually explaining what Shock and Awe is really intended to do.
The goal of Shock and Awe is not to cause a massive civilian death toll, nor is it to create a situation where mass civilian deaths are inevitable due to pandemic disease or famine. Doing these things is horribly wrong, and it is also militarily useless. Therefore, a rational military will refrain from these things even if it is totally amoral, and a military that is moral will refrain from these things even if it is largely irrational. The US military may or may not be moral; this is a matter widely debated. It is, however, certainly fairly rational.
Instead, the goal of Shock and Awe is to create a feeling of "Oh my God! How did they do that?" in the opposing nation. Ideally, this will cause them to run away or surrender rather than fight you, which generally results in fewer people getting killed.
The preferred method for doing this is a massive show of air supremacy, demonstrating that you can drop as much raw firepower as you want anywhere you want and no one can stop you. The idea that one could be destroyed by fire from the skies at any time is rather intimidating, and can sometimes achieve the desired 'Shock and Awe' effect nicely.
Towards this end, the US military might use a hailstorm of cruise missiles to destroy a bunch of infrastructure in the enemy nation's capitol, preferably all at once. If this happens all at once, the enemy now knows that the US can throw not only one, but fifty cruise missiles, effectively all of which will hit and destroy their targets. Preferred targets for attacks like this are bridges, power plants, and other facilities that cause large-scale and immediate inconvenience to a lot of people. If you're doing thing morally, you pick targets that will cause a lot of inconvenience without causing a lot of deaths. Hospitals are an example of a bad target, because their destruction won't cause immediate problems and because blowing one up means that a lot of civilians are going to die in the near future. Carrying out the bombardment at night may help a great deal, because most major buildings are largely empty at night.
On the battlefield, Shock and Awe takes on a different form. For instance, let's say that you wish to defeat an entrenched line of Iraqi infantry divisions without the messy results of a direct melee. Under Shock and Awe, you might proceed as follows: drop one extremely large bomb on one portion of the line, followed by propaganda leaflets all over the rest of the line. The extremely large bomb Is probably something like a fuel-air bomb which creates a truly gigantic and scary fireball; the leaflets read something along the lines of "Hi! This piece of paper could have been a bomb, but this is your lucky day! You might want to consider surrendering now, before the next squadron of bombers flies overhead!"
In both these cases, the goal is to demoralize the enemy as much as possible without having to destroy them entirely. This is not always practical, which circumscribes the usefulness of 'Shock and Awe' doctrine. But when it is useful, it can be very effective as a way to win wars without losing lots of your own soldiers.