A military character
Question: How would you write a story that is based on a character that just came home from the war, especially when you know next to nothing about someone coming home from a war?
There are several short answers to your question that spring to mind...
1. Why are you writing about a character you have no knowledge about? Many writers, especially those of literary fiction, would say you have no business doing so. (I don't necessarily agree with this point of view, since it dismisses all fantasy and science fiction, plus a good deal of historical fiction. Nonetheless, they have a point about the importance of authenticity.)
2. Find out about what it's like to be a soldier coming home from war. Talk to veterans, if you can. Do some research on the subject. If your story is set in the past, you may be able to read diaries and letters written by veterans of past wars. Talk to a research librarian about this.
3. Use your imagination. This does not always work, but it can yield tremendous results if you are determined. If possible, try to combine it with some research or interviews, because there are areas where your imagination may fail you.
Bear in mind that while it's one thing to create a story that seems realistic to someone who is not a veteran, it is much harder to write a story that veterans will find authentic. But regardless of your audience, you want to create a story that will have the "ring of truth."
Also, keep in mind that you are not writing about the generic experience of all veterans, but the unique, specific experience of one fictional veteran in particular. So you can make up some things.
Best of luck.