What is the process to have someone enlist while on DACA (Deferred Action for Childhood Arrivals)?

They have to be a legal US resident to enlist.

This is how a DACA recipient can get a green card:

Can DACA Recipients Apply for a Green Card?
Yes, it is possible for DACA recipients to apply for a green card if they meet the lawful entry requirement. If you've entered the U.S. lawfully with Advance Parole or if you first entered with a valid visa, you may meet the green card eligibility requirement. The most common green card types are family-based, employment-based, and humanitarian. The following sections of the article will explain the opportunities that do or do not exist for DACA recipients to get those green cards.

That's the first result I got when I Googled it.

If they don't have a green card, they're not enlisting.

You must be a legal resident to join the military, that means having a Green Card.

SGT Rodolfo Chavez , I responded to your DM