The U.S. Army has been studying its experience in Iraq so far, to determine which methods were more successful. One important lesson is that it's more effective to have Americans teaching Iraqis how to fight, than having Americans doing the fighting. This despite the fact that Americans are much more effective in combat than the Iraqis.
The U.S. Army has over a century of experience in dealing with situations like this. And that has taught the army to seek what the some major differences that exist in each nation where American troops are involved. For example, in Iraq, religion, tribalism, corruption and a poor military tradition are all key factors.
Religion is only an issue insofar as it provides a reason for the for the Sunni and Shia Arabs to hate each other for so long, and so much. The Kurds are also at odds with all the Arabs, but especially with the Sunni Arabs. Religious and ethnic differences are not unique, but in Iraq they are particularly intense because, for the last three decades, the Sunni Arabs were particularly brutal rulers. Now many Kurds and Shia Arabs want revenge.
Tribalism and corruption tend to go together. With no tradition of effective central government, most Iraqis depend on tribal organizations to take care of basic security and dispute settlement needs. This means that the first loyalty is to the tribe, and anyone elected or appointed to national office will be under tremendous pressure to look after the tribe at the expense of the state.
All of this made it difficult to even recruit Iraqis for a national army and police force. So the fall back plan was often used. That was recruiting units that had troops of all one religion or ethnicity. That meant lots of battalions that were nearly all Shia Arabs or Kurds. As a result, these units would easily get out of control when operating in Sunni Arab areas. Not that this made a lot of difference, as it would take a generation or so for the enmity between the Sunni and Shia Arabs to abate anyway.
But the biggest problem with Iraqi troops is training. In the past, the Iraqis used brutal discipline, and endless drills to train the troops. This doesn't work as well as it used to in centuries past. Soldiers now have to be able to think, and think fast, to win on modern battlefields. In the past, Iraqi leaders did not like their soldiers to think too much. So how do you change all this?
The U.S. Army has well developed routines for American troops to use when training foreign soldiers. But for the Iraqis, the problem was not learning new tactics and techniques, but how to think in combat. This was best taught with constant reminders, and close contact between the trainers and trainees while in combat. The U.S. Army typically does this by assigning a training team of ten American NCOs and officers to each Iraqi battalion. But experience has shown that ten Americans is not enough. Using up to 75 Americans per Iraqi battalion gets much better, and quicker, results. The problem with this is getting enough American troops to volunteer for this kind of work (you need eager volunteers to make this effective). You also need lots of translators. It would be better if the Americans spoke the local language, and the U.S. Army Special Forces have shown the effectiveness of that approach. But few Americans speak Arabic, there are not enough Special Forces to meet the demand, and you can make this work through an interpreter.
The American advisors don't just pass on military tips, they also point out how important it is to get rid of the corruption, and to adopt a real national consciousness. While most Iraqis denounce corruption, in practice, they either take part, or look the other way. That doesn't work. You either have a majority of the population actively against corruption, or you never have a country that works. This includes the military, where many Iraqis see nothing wrong with betraying their fellow soldiers if the bribe is large enough. That is slowly changing. The best Iraqi units are not only competent in essential combat skills, but also able to act independently in battle, and resist threats and bribes from terrorists when they are off duty.