Pick up your iOS device of choice (feel free to use whichever hand you like), and open up the Apple Music app. So far so good.
Hit up the face icon in the top left, and you'll be presented with your account page, after which you should tap on 'View Apple ID'. Enter your password, and boom, you've just hacked into the mainframe.
From here, press 'Manage' in the subscriptions area, and you'll have a list of all of your subscriptions. Hit up Apple Music, and slide the 'Automatic Renewal' option to 'Off'.
Congratulations, you have nullified your Apple Music trial, and you won't be charged unless you flick that switch to 'On'.