I primarily want to know about the later Aztec armies who would have fought the Spanish conquistadors but any other information about other periods or civilizations is welcome.
In order of importance I would like to know:
The method(s) of recruitment
The size of the military relative to the civilian population
How troops were equipped
How were troops organized (What was the chain of command, division types, etc)
was there a (in)formal military doctrine. If not was there still a common set of tactics
I wrote a comment a while back generally covering many of these topics with regards to the Aztecs, which also references a few other older comments. As corollaries, I might also include comments I've made on conquistador armor and the Battle of Otompan. I was also an early guest on the AskHistorians Podcast (which I now host) speaking on the Spanish Conquest (part 1, part 2). That was back when we were still figuring out what the podcast would be and how, so those episodes are a bit rough.
If any of those comments leave you wanting more, I'd be happy to field follow-up questions.
For recommended sources, Ross Hassig is the preeminent scholar of Aztec military matters. His Aztec Warfare is a seminal text and his Mexico and the Spanish Conquest is an excellent work as well, particularly as he deliberately takes a critical approach to the primary sources.