The first thing that can be done to prevent the theft of artifacts in Iraq is to take everything that is already exposed and put all of it in a highly secured area. This way it will be much more difficult for people to get a hold of it. If its not easily seen maybe people will be less likely to attempt to steal it.
Second, the sites that are known to archaeologists to have artifacts should be heavily sealed off from anyone without proper identification. There should be not only heavily armed guards patrolling the perimeter of the sites but also some sort of physical barrier protecting the perimeter of the site. Guards should be fully armed with working up to date equipment. The use of video monitoring and motion detecting lasers should also be employed around the perimeter.
These guards should probably be a trained branch of the Iraqi military.
Third, there needs to be some sort of education system to teach Iraqis how important these artifacts are to their history and culture. That there more than just objects that can be used for monetary gain.This should be done at a very young age so by the time the children who are growing up now are adults they will possibly have a greater appreciation for their past artifacts than maybe their parents did.
Finally, probably one of the greatest things that could be done to avoid the looting of these sites and thus protect the artifacts is create a whole bunch of decent jobs fast. Id imagine if many of the looters had jobs that could support themselves and their families they would not feel the need to loot these sites. Not that all the looters do it to provide for themselves but i'm sure it would still help a great deal.