iTunes Radio is a free for all iOS users. The service is supported by ads. This means you do not need to pay any monthly subscription fees or pay to download any songs, unless you want to own them.
To access iTunes Radio your device needs to be running iOS 7 or later. You can find the iTunes Radio tab in the Music app on your iPhone or iPad. Just tap the tab and you'll be given a list of available stations. You can also create your own stations by tapping the box with the giant red X labeled "New Station". From here you can create a new station from a list of genres or use the search bar to enter an artists, genre or song.