I would imagine that it’ll work much like flu shots - employers and health care providers will manage / provide that.
So initially, it’ll be health care provider companies providing it to their own workers, along with employers like cities/states/counties providing it to their first-responders and other essential employees. Later on, they’ll have a vaccine event and offer it to their public facing employees, and then finally a third round, where they’ll offer it to their accountants, system admins, and other non-public facing employees and their families.
I’d think the elderly/high risk would work similarly- it’ll be through health care institutions and providers- possibly they’ll even call people and suggest they come in for visits.
As for the scheduling, I don’t know that it’s been worked out yet even in broad strokes, other than the large-scale categories.