They were quite the regional military power for some time, controlling big chunks of the region that is modern-day Thailand, Laos, Cambodia, and Vietnam.
Carvings in the historic temples depict soldiers with spears, bows etc, and the use of war elephants and river boats.
But my question is how did they make their army? Were they a standing force, or just peasants called up in times of war? Was there a system for providing training and equipment?
And what kind of command structure was there?
This is way outside my specialty but it is a cool question and I don't know if there are SE Asia flairs here so I will give it a go. I'm basing this off of Thailand: A Short History by David K Watt, which deals with Angkor in the first part of the book, A History of Southeast Asia: From Prehistory to History ed Peter Bellwood, and the Cambridge history.
To start, SE Asia is exceptionally diverse--to give an example, there are four major language families in the region: Austronesian, Austroasiatic (perhaps the "most indigenous" family), Sino-Tibetan and Tai-Kadai (as a comparison, Europe is almost entirely Indo-European, with pockets of Basque and Uralic). This can be explained through both geographic and political factors: the rugged landscape naturally separated human populations, and the expansion of the Chinese state to the north pushed different populations down into SE Asia.
This is relevant because the images depicting the royal armies of Angkor tend to show an exceptional diversity, with ethnic markers of Tai, Mon, Shan and other identifiable groups. Many of these groups, such as the Tai (who were "hill tribes" at this point), were not under the direct control of Angkor so we can infer that the armies included large numbers of mercenaries and auxiliaries. Also worth noting is that SE Asian states were fairly loosely organized: the common metaphor used is that they had a mandala organization, essentially concentric rings of importance and influence. The farther away from the capital, the less tightly bound to the central administration. Unlike modern states, Angkor did not have extensive bureaucracies enforcing writs of law it demanded tribute and homage, and in return granted protection and shares of the spoils. Outside of these, communities would be largely autonomous, and recent archaeology has done a great deal to argue against the idea that the king was a God King whose word was divine mandate throughout the land. It is highly unlikely that Angkor could have maintained a large standing army even if it wished to.
In comparison to other empires (such as the Assyrians) we can assume that there was a sizable "core" standing army, but beyond that it would have largely been ad hoc and made up of conscripts and, particularly, mercenaries.