Somewhere in one of Dorothy Sayers' books is a discussion of understanding art (painting). The things she says apply equally well to music, I think. The first step is to expose yourself to a lot of it, both 'good' and 'bad'. Over time, with careful observation, the good will become more readily apparant. And never forget that art is about communication. If it says something hateful but does it well, it's still art.

The greatness of music is that it can take us out of ourselves. It can show us depths of feeling that we were unaware of, that we may even find unwelcome. The weakness of music is that the process is aided immensely by better understanding. A person who plays or sings or has studied instruments/theory has a huge head start over any one who hasn't.