As promised, Apple launched its new music streaming service on June 30, 2015. The service offers both a free and paid option for all iPhone and iPad users who upgraded to iOS 8.4, but using the free tier can be a bit confusing. Users must sign up for the free 3 month trial period to access any of the Apple Music features. This means you must disable the free trial option if you do not want to pay $9.99 a month once it expires. Here's how:
You can disable the automatic renewal of your free trial by going to the iTunes & App Store section in the Settings app on your iPhone or iPad. Tap your Apple ID or log in to your Apple ID, then tap View Apple ID from the pop up box. Scroll down until you see "Subscriptions" and tap Manage. Tap the the Automatic Renewal slider so it is OFF. You will now be able to use the free tier of Apple Music without being charged $9.99 in 3 months (September 30th if you signed up today).
The free tier of Apple Music allows you to listen to Apple Music radio stations, access Beats 1 and follow artists on Connect. You can see a complete rundown of the differences between the free and paid services here.
You can always upgrade to the monthly $9.99 single user plan or $14.99 family plan from the Music app or Apple Music Membership settings, if you want to keep the advance features of the service.