How does the author choose to tell his story and how does that inform you about the act of remembering war ?

With The Things They Carried, the chronology and the way the story is told are extremely important. Tim O'Brien has not put the short stories in a linear order, but they're not random either. It may seem that way at first, jumping from one character to the other, from past to the present to even further past, but it's a carefully considered system. It allows the reader to grasp the essentials first and gradually move on to other tales, some of which require a deeper understanding of the situation and the mindset the men are in.
It also represents how disjointed and treacherous memory can be when dealing with traumatic events. Several times, the author notes how in the present he wakes up in the middle of the night, remembering snippets and pieces of events that may or may not have been real. What he is dealing with is not just his own memory playing tricks on itself, although that happens as well. O'Brien dedicates a lot of thought to how some things simply can't be remembered correctly, how memories take on a life of their own the second they've happened and grow from there until they're almost unrecognizable. He draws attention to a soldier's need to sometimes add details to make the story more interesting, or to hide things that are too painful to speak about honestly.
One of the more profound ideas is that if you know the source material—in this case, the Vietnam War —well enough, you can conjure up a "truthful" story that never happened. That is to say, you can write a fictional story with fictional characters, but if you get all the details and the setting right, it may as well have happened to someone. It probably did. That could very well be the case of a lot of stories in The Things They Carried. Does it make the stories any less true?
There is a particular scene in the book where one of the men, Curt Lemon, steps on a mine and is killed. Most of the others are close enough to witness it from some angle, but memory immediately becomes false. It's natural for humans to think that events make sense, that they happen in a certain, logical way. It's why we embellish stories, but why we also don't go overboard with it. If O'Brien has added some poetic devices into his stories, the reader wouldn't know, because it's not like anything supernatural happens. Therein lays the problem with Curt Lemon's death. The author can't take his own memory seriously, because it seems a little "overdone" for him. The way the light shines like a beacon, the way he thinks he sees the expression change on Curt's face—it's hard for him to believe it, so he can't imagine the readers could. Yet, he says, that's how it was.
The Things They Carried is full of stories, some of which sound plausible and others outright fantastic. Since the author himself talks so much about false memories and how no war story could be honestly believed, he turns himself into an unreliable narrator, which is intentional. It implies that war should be read about as it is remembered —with suspicion, with a good deal of doubt, with interest and compassion rather than stone cold criticism.