The quality of an asteroid belt or ring will be displayed in the same manner on the system map when you select the belt or the planet the ring is orbiting. To have that information, you need to have purchased it from the cartographer's shop, or to have run a detailed surface scan of the object in question if you found it yourself (not 100% sure on this, but this is how I remember it).
In other words, if you go to an (to you) uncharted system, and discover some planets with planetary rings, you will not know their composition unless you also have a detailed surface scanner. And you currently cannot detect the quality of uncharted belts since you cannot use the detailed surface scanner on belt clusters, last time I checked.