Well, I actually received a link from my employer to sign up. I'm only 26 but I work for an organization that serves one of the most vulnerable populations...the elderly. The link provided time slots for the local county health department, which I had to quickly sign up for to reserve an appointment. I get my second shot in exactly a month (I received Phizer). They set up the 2nd appointment for me while I was there.
For someone who doesn't work in an organization like me or isn't a first-responder, they have it opened to those who are 65 and older now. I'm pretty sure all they need to do is be registered with the health department, and someone from the department either calls or emails people to get the appointments set up.