Recognize the basic music genres. For example, do not get caught up with "pop punk," "indie folk" and "jazz fusion" at the outset. Maybe down the road you can unpack some of those subgenres, but the first step is learning the basics. The main music genres may be found categorized at your local record store. Generally, these basic genres are "rock," "pop," "classical," "jazz," "folk," "world (international/latin/reggae)," "hip-hop (rap and R&B)," "country," "electronic" and "experimental/avant garde."
Listen to the most popular artists from each genre. The clearest way to hear the differences in style is by listening yourself. So for "classical," listen to Beethoven, Mozart and Stravinsky. For rock, listen to The Beatles, The Who and The White Stripes. For hip-hop, listen to Tupac, Kanye West and Jay Z. And so on like this. The easiest way to do this is by going to an online music store to listen to all of this music. Expect to put hours of study time into learning about genres.
Take note of what you hear. Disassociate yourself from your tastes and simply hear the music that is being played. Notice that folk singers often play acoustic instruments and that jazz music may seem random. Once you're able to put a song on at random and easily recognize its genre, you're ready to dive into subgenres. But because there are countless subgenres, this is a feat you must perform at your own risk. Music fusions are endless, and if you attempt to follow them it will become a never-ending task. But as long as you keep your mind open and allow yourself to think critically about the music you're hearing, you will be able to learn much about the wealth of genres that are available today.