The various stories, represented as chapters in O'Brien's The Things They Carried, all tell a different angle, a different experience or event in the Vietnam War. At times it reads like a short story, with characters introduced and developed, while in others, O'Brien starts off and continues with the first person "I".
At the beginning of Chapter 3, in the first paragraph, O'Brien writes:
"For instance, I remember a little boy with a plastic leg"
The story begins, in other words, with O'Brien telling us what happened, and the "I" never changes to another character. It is through this kind of indirect method of writing that we come to see him as the narrator of the book, so much so that even when other stories do have characters, we get the sense that O'Brien is in the thick of them, and by the end of the novel, we're pretty sure all of the stories are about him in some way.