When the new emperor came to the throne the message would go out to all the mints in the empire to start manufacturing coins with the new emperors image on it. the closest one to you would probably be in trier. It might take a couple of years for the news to filter through to you but eventually you would see a denarius or whatever with Gallienus' face on it such as this one.

There are of coutrse other ways, imperial proclamations etc. but I do not know enough about them to give you a full an detailed response.