In 2004 I went through a book my sister bought for her son, a book on modern popular music in America. After that I began to do more reading, mostly on Internet, on different genres of music in America after 1900. Not only that, I also constantly listened to whatever music I was reading about, via CD, radio, Internet while I was driving, surfing the net, doing my work...
So nowadays I'm able to tell which singer or band belongs to which era, plays what kind of music, and even who has composed or performed which piece of music.
I learned the same stuff about western classical music by a shortcut, much earlier, when I was in college. I simply took a course in Music Appreciation.