To give a rough overview (thank you, Wikipedia!), the basic principles of classic Just War theory, in terms of going to war (or, if you want to get all fancy and latin, jus ad bellum), are
Just causeOne of the things I've been thinking about is that I'm not sure I would want to live under a completely pacifist government, a la the Quakers, the wonderful Society of Friends whom I admire so much, who, in the strictest construction, won't fight back even when attacked. I do want a government that would be willing to come to my defense as a private citizen. With that in mind, I have to say I think it is a burden laid upon leadership to defend its citizenry in a thoughtful and just way.
The reason for going to war needs to be just and can therefore be recapturing things taken or punishing people who have done wrong. A contemporary view of just cause was expressed in 1993 when the US Catholic Conference said: "Force may be used only to correct a grave, public evil, i.e., aggression or massive violation of the basic human rights of whole populations."
While there may be rights and wrongs on all sides of a conflict, to override the presumption against the use of force, the injustice suffered by one party must significantly outweigh that suffered by the other. Some theorists such as Brian Orend omit this term, seeing it as fertile ground for exploitation by bellicose regimes.
Only duly constituted public authorities may wage war.
Force may be used only in a truly just cause and solely for that purpose—correcting a suffered wrong is considered a right intention, while material gain or maintaining economies is not.
Probability of success
Arms may not be used in a futile cause or in a case where disproportionate measures are required to achieve success;
Force may be used only after all peaceful and viable alternatives have been seriously tried and exhausted or are clearly not practical. It may be clear that the other side is using negotiations as a delaying tactic and will not make meaningful concessions.
The anticipated benefits of waging a war must be proportionate to its expected evils or harms. This principle is also known as the principle of macro-proportionality, so as to distinguish it from the jus in bello principle of proportionality.
It seems to me that the importance in just war theory is not in proving "why we are right to go to war." Instead it is because in a fallen world, wars do happen and it is important for people of faith to be at the table in some meaningful way, other than saying, "Wars are bad."
The other thing is that Just War theory is actually a theory of interpersonal conflict writ large. One of the reasons I think it would be helpful for us to understand Just War theory is so we can apply it, say, in the case nasty office politics or, you know, church politics. Change "going to war" (or "force")to "confrontation" or "taking legal action" in the jus ad bellum above and see what happens.
In that vein, I remember once running across a parody of Just War theory called the Just Adultery theory. It was supposed to make me see how the Just War theory is merely a pretext for going to war. Unfortunately, even while trying to make it sound bad, the Just Adultery theory makes a reasonable point (i.e. 1. Last Resort. Every other means of getting along must be tried: discussion, advice of a third party, reconciliation of differences, expressions of affection, anything short of adultery.) Given that Jesus says in the gospel of Mark that "A man who divorces his wife and marries another woman commits adultery against his wife. In the same way, a woman who divorces her husband and marries another man commits adultery," the Just Adultery theory seems to have very practical applications.
Now, I know I'm being the devil's advocate, here, but believe me, I'm not saying that we should be in Iraq. I don't think we met any of the criteria from jus ad bellum to go to war. Not one. For that very reason, I think people of faith are better prepared to meet the argument of those who claim to be fighting a just war if we know what terms are being used or abused. "War is bad" will cut no mustard.