Make sure to take a screenshot of whatever confirmation you get. Because servers are overloaded, some people in my area did not get confirmation texts or emails.
If somebody is elderly, the chances of them getting an appointment is extremely low without the help (and extreme vigilance) of their tech savvy children/nieces/nephews.
Some states have also opened up their registrations to people 16+ with serious chronic health conditions that put them at high risk of severe COVID-19. In a handful of these states, many of these people have received a vaccine. But, it is first come first serve, which is an absolute disaster along with being inequitable.