'War records' as such aren't really a thing for the majority of human warfare, but all such books and academic papers are based on sources dating to as close to the battle as we can possibly manage. As literacy increases and armies do more paperwork, we have more and closer accounts of battles. For an idea of how they did it in the ancient world, u/Tiako examines how we know how Cannae went. A lot of the Classical works are even freely available on the web; Tiako cites Polybios' Histories 3.113-116.

Bouncing off that post, it's really the same way for most other battles in most any period, with the biggest challenge being lack of sources, or how to reconcile different accounts of the same battle. (Again looking to the Classics, the Battle of Leuktra has a surprising four different accounts...and no way to allow for all of them to be true.) That's where the milhist people earn copious stacks of money fall into acrimonious argumentation and debate.

Of course, just because we have more source material to work with now does not mean that we're now invulnerable to getting it wrong. (If you'd like to know more on this detail, ask me about Midway and why Fuchida Mitsuo is a lying liar who lies.)

And of course, if anyone else would like to contribute further, please don't hesitate to write up! More posts are always, always welcome.