Robin Hicks ⋅ Naperville, IL BP ⋅ 41 years experience

Earnest, Building some on what Rebecca offered. I recently attended a presentation at a University given by personal coach Rob Sullivan who gave this advice.
Be the first to tell your story. Relate a situation you were faced with, what actions you took and what the impacts were. Not all outcomes have to be positive (but positive is a good re-inforcer), as long as you demonstrate you've learned, grown and/or adapted from the experience.
Let people know there is little risk in hiring you (it's the risk they're afraid of), and that bringing you on board is actually the next logical step. Convince them you've thought about the job you want and share what steps you've taken to do something about getting the job. Given them a reason that shows other people value what you bring to the table. When selling your worthiness to a prospective employer, let your passion, initiative and resourcefulness shine through.
So prepare several stories to keep in your 'back pocket'. Each should include examples of your skills/abilities so you have them ready to relate during that next interview. For example: While in school a young person was the top fundraiser for a local non-profit. They demonstrated great organizing and speaking abilities, were able to positively influence people at various levels, and pursued goals for the non-profit with passion. As a result received an award from the non-profit Board. These skills will be applied to your company when you give me role x because I want your firm to be as successful as it can be.
Good luck.

Rebecca Splinter ⋅ Tacoma, WA Wells Fargo ⋅ 40 years experience

When changing fields (as you will be: from military service to another industry) it is challenging to do so at the same level of role. You may need to expect to take a step back in terms of the accountabilities assigned to you, so you can learn the things that people in the roles you want have learned. However, even taking that step back, the pay level may be equal to what you earn in your current role. At least, that's what I've found in discussing specific job choices with others I've mentored who were leaving military service for a private sector role.
After you factor the foregoing into your thinking about the jobs for which you apply, then your primary focus should be finding experience you have that is a good match for skills and accountabilities listed in the job posting--and including that in your resume. For example, if a job posting asks for 10 years of experience with X equipment, research that equipment to find how it is similar to the equipment you have great experience with, and include that in your cover letter.
I hope that's helpful. Not sure it's on point since I don't know what field you are targeting. I'd be happy to talk if you'd like. (I've been in HR for decades.)

Rex Conger ⋅ Gilbert, SC Perry Memorial Hospital NR NH Pensacola ⋅ 50 years experience

My suggestion is for you to clearly identify the career area(s) that you would like to pursue. Once you have identified your targeted career fields then you need to begin to network and get your foot in the door.

Common methods are - Non or Paid Internships and Volunteering. Participating in Internships and volunteering gives you and the potential employer the opportunity to learn about each other. Either approach shows interest and gives you the opportunity to network inside an organization that you would like to work in. It can also give you experience and demonstrate that you have the experience they are looking for.

Best wishes!