How can I relate military experience on my CV to jobs in the private sector?

First of all, see the military environment in the same light as any other employer. You may have done several courses that can be listed, received awards and promotion because of good conduct or leadership skills, presented classes or training and worked with technological applications. List soft skills applicable to the job that you are targeting, for instance, self discipline, motivational abilities, communication skills and leadership abilities. Although the software applications may differ, you can still list computer literacy, working with heavy duty equipment, stock or record keeping, budgeting etc. Stay away from strictly military terms and make use of current employment vocabulary.