The data is stored as coordinates, so given software that supports a projection and understands the system used to store the data, it can be transformed.
(Much recently available data is stored using geographic coordinates - basically the latitude and longitude, and maybe the elevation, but a lot of older data, and especially government data, is stored in coordinate systems that are designed to limit the error in spatial analyses that are done on the data. This isn't really something that you would have to understand deeply to make a map in a given projection, but you might have to deal with it along the way.)
(Much recently available data is stored using geographic coordinates - basically the latitude and longitude, and maybe the elevation, but a lot of older data, and especially government data, is stored in coordinate systems that are designed to limit the error in spatial analyses that are done on the data. This isn't really something that you would have to understand deeply to make a map in a given projection, but you might have to deal with it along the way.)