This is actually a somewhat broad question and you could get many possible answers. I'll only discuss one thing and allow others to pipe in.

In 1863, Abraham Lincoln signed a set of rules on wartime conduct that his troops were going to follow. This was called informally the Lieber Code.

It was named after a German-American named Franz Lieber who had fought in the Battle of Waterloo when he was fighting with the Prussian Army. Lieber ended up as an academic and eventually was a professor at Columbia.

Anyway, him and several other guys got together and came up with this code. It addresses several things that would later be incorporated in The Hague Conventions and Geneva Conventions.

It's starting point is that the means must be justified and codified so that soldiers don't end up making terrible choices in the fog of war. You have to begin with the end in mind and that your goals in war must be reflected in your conduct. It explicitly banned a few things. Here are a few:

1. You can't kill POWs.

2. Torture can't be used to get a confession.

3.Poison can't be used.

That's just some, but you can see how those became part of later war conventions. Lieber also differentiated between POWs and Guerilla fighters. POWs needed to have uniforms, a command structure, and a capacity to hold other POWs. Without that, the Guerilla fighters would be executed, though Lieber didn't really endorse that. But similar rules made it into The Hague Conventions and Geneva Conventions.

The Lieber Conventions also outlined the treatment of occupied territories and the status of slaves, escaped slaves, and returned slaves.

It did a lot more than that, but that's just the basics. The Code wasn't really put into that much use during the Civil War as some Union generals and Confederates didn't really consult it. It's importance became more evident when the Europeans adopted quite a bit of it later and it worked it's way into future conventions and whatnot.

I second /u/GregPatrick: the law of war has developed many times in many different places, such that there are many ways to answer this question depending on which culture and era you highlight. One thread you might take a look at is this discussion, about nine months ago, about "just war" theory and "illegal wars" in Roman history, especially towards the end of the Republic. In brief, Roman tradition held that certain rites be followed before a war could be lawfully commenced. But these "rules" were mostly honored in the breach. This of course is about "just war" theory, which overlaps with but is not the same as "war crime" theory.

For war crimes, consider this thread that expands upon GregPatrick's comments about the Lieber Code and the Geneva Convention.

An interesting topic that someone with WW2 flair might discuss in greater depth is the public idea of war crimes, and how those ideas evolve during actual war. For example, there's a recent Radiolab episode about American public opinion of war crimes during World War II. And I believe there's also some controvery, for example, about whether Churchill was prepared to use mustard gas in the event of a German landing. Since that is outside my specialty, I pose it only as a recommendation for someone to follow-up on if they want.

The first line of thinkers in this tradition exist within the Roman and Greek society. Cicero, Plato and Aristotle wrote about the moral issues facing leaders and soldiers when they go to war.

A lot of it also comes from the Christian Tradition of Just War. Important first authors on the tradition were St.Augustinus and Thomas Aquinas.

It was thought out to find a balance between warfare and the christian pacifist origins.

The first important secular thinker on just war and the 'laws of war' was Grotius. He also wrote a lot about international lawmaking.

Outside the Christian tradition there are a lot of other examples of 'laws of war'.

Sun Tzu for example stated that a general should treat is prisoners wel. This was more out of a pragamtic vision since Sun Tzu saw it as a way to gain more manpower. More important here are Mo Tzu and Mencius who wrote about the injustices facing people and the necessity at times of taking up arms.

In Indian society there are discussions to be found about ethics of war in The Laws of Manu and The Bhagavad Gita.

Another example from the Talmudic law from the 12th century involves sieges. It said that the besieger should leave space open from the siege so the civilians could flee from the city.

As you can see the laws of war developed separate in every society. So im not so sure how they did develop, but i would think that a lot comes down to religious authors.

source: Moral Constraints on war

if anybody has any questions on just war theory ask away. I just wrote a casestudy for my thesis using just war theory.