Cannot able to subscribe free trial without paying! Please help

You need to have a payment method attached to your Apple ID to join, so you won't be able to join without one. But don't worry, it won't charge you when you put your credit card number in, it will just start the three-month free trial. At the end of those three months, it will charge that payment method to continue a monthly subscription unless you turn off auto-renewal. Thankfully turning off auto-renewal is easy, just follow these steps:

From within Apple Music, click on the little red head in the top left-hand corner. Then click 'View Apple ID'. From there click on 'Manage' under the subscriptions, then 'Your Membership - Apple Music Membership' and then turn off auto-renewal. You won't be charged unless you choose to manually continue your subscription after your free trial ends.