While The Things They Carried is a compilation of short stories referencing the Vietnam war, the stories center around recurring key figures and, most importantly, O'Brien's narrative structure of analyzing the concept of truth versus fiction as he repeatedly breaks the fourth wall. He blends truth and untruth in his retellings to work through his own difficult war memories in hopes of finding peace for himself and his friends through his writing. Here are a few ways in which you can break down the story to create a logical summary.
Start by focusing on O'Brien as an author, illuminating the reasons for writing this compilation of stories. O'Brien himself is a Vietnam veteran drafted into a war he didn't believe in. He writes about his experiences to help him process the trauma he suffered along with toeing the line between fiction and nonfiction to protect himself and his platoon.
Next, talk about O'Brien as a character, highlighting the details that connect to his account of the war. This pathway easily connects to the other recurring characters in the stories, such as Cross, Lavender, Bowker, Riley, Kiowa, and more. By bringing in the other characters, you can touch upon major events in the book, such as Cross's love interest, Bowker's suicide, and Lavender's death. There is so much more to say, so write what stands out to you as a reader.
You could also think about the book as one big story, even though it's broken up into separate, disconnected chapters. Each chapter is connected through time—past, present, and future. You could start with the events that occurred before the war, talk about some key points during the war, and end with the aftermath when the men return home. However, if you select this option, be sure to introduce O'Brien as a writer, his background, and his main purpose for writing.
There's no one way to write this type of summary. Check out the link below to help you structure your piece. Happy writing!