Turn on your radio. It's becoming harder to find radio stations that play big band music. Many oldies or satellite radio stations have certain times of day you can listen to big band music. Check your radio station's listings online to see when or if they have airtime devoted to big band or swing music.
Listen online. There are many online radio stations that play nothing but big band music. Search the Internet and you might be surprised at how many options for listening you have.
Experience the music live. The best way to hear big band music is in person. There are a lot of big bands who tour the United States and play in large and small venues. Pick up your local newspaper or weekly entertainment newspaper and look for listings for big band performances. You may have to travel to a bigger city in your area, but the drive will be worth it.