Do detailed research upfront.
Are you thinking letters of recommendation for your elected officials’ noms, and have you researched each of their websites to see what they require, format, due date, etc.? These processes can and do vary among all elected officials.
I believe USNA requires evaluation forms filled out by specific teachers in certain subjects online via a link, but the primary source is your best answer. This is an area I am weak in, not having seen the current application in a portal. Have you read every page, link and hamburger menu item at USNA.edu, taken notes, identified action items, started working on a timeline?
Once you are armed with facts, then you can speak knowledgeably about your request. Be respectful of their time and schedule, and ask if you can have 15 minutes to let them know about some upcoming college-related tasks. If you don’t think they are familiar with the Service Academies, you could do a little one-pager hand-out with some bullet points on the mission, the fact you get a BS degree at a highly-ranked institution, and a guaranteed career as an officer after graduation, your goals, etc.
Learning how to articulate a request, express key points and action steps orally to people in authority is a core officer skill. No time like the present to start - you can do this.