Dianne, As far as I understand it, you can listen to up to 250 songs that you have downloaded from Amazon's digital music store without it affecting your storage capacity, but I believe you need a wireless connection. And if you want more space, you can buy a plan that allows you to have up to 250,000 songs. Furthermore, if you have an Amazon Prime account, you can stream music to your Fire (in the same way as you would stream Netflix), but you have to have a wireless connection.
Also, you can download the Pandora app, set up an account and listen to music for free (but you have to tolerate their ads.) And there are other free music apps available as well. I hope this helps. Sharon