Ha, I could write a book on this!
Not sure what industry you are applying to, but as a Veteran, you would be well advised to apply for federal jobs.
That said, I am a federal (law enforcement) supervisor who has been a part of the hiring process many times. Prior to this, I was on hiring panels on a city PD and a corporation.
While we in the federal world are bound to not say what goes on behind those closed doors, I can tell you this...don't sell yourself short! That is the #1 thing that holds people back.
For example, we use checklists of things we are looking for when reviewing resumes-- and what we hold in our hands are precisely the resumes that you fill in on UsaJobs.com or similar sites, we just print them from there. I cringe when I see someone that myself and the rest of the hiring panel unanimously agree would most surely be an awesome candidate, but we can not proceed because their resume did not contain the right things we needed to see to score it higher. We can not assume anything, we need to see it in writing to give you credit.
Specifically, something like this...person for an entry-level LE position who is a Veteran and now works as a supermarket produce manager. Candidate spends just TWO LOUSY LINES of space discussing his military experience, even though it was twelve years in the Guard with several deployments, NCO schools, etc. We see this, and we know this person is probably someone that we want, but instead he felt it was more important to spend A WHOLE PAGE writing about his accomplishments at the supermarket! We can give him points for, let's say, taking the supermarket's management classes, however we don't care about 99% of the other words he writes about that job. That person just sold himself short and dropped out of the race because of a resume that concentrated on the wrong things.
Anyhow...be succinct but thorough. Your resume does not have to be dry and boring and super-formal. You can creatively phrase concepts like teamwork, leading by example, etc. Tell us the schools you went to, describe your duties. Maybe you were an 11B who sometimes pulled gate guard duty-- mention that! Did you also search vehicles at the gate, or check IDs in databases? Mention that too!
Did you go to some odd schools? Tell us! Voluntarily added a skill? Looks good and shows initiative! Save all of those certs that you get, Lord knows I have, and it paid off for me.
You can private message me if you want, as I mentioned I could write a book on this topic. Being an Army Veteran myself, I know how tough it can be to translate military experience to marketable civilian skills. And I swear it can be done, no matter what you did in the military!