how do I start to use apple music on iPhone

After you tap Search at the bottom of the Music app screen on your iPhone, and then tap in the Search box at the top, did you tap Apple Music at the left of the screen just below the search box?

Also, are you subscribed to Apple Music?

Open the Music app on the iPhone. Also see: Join Apple Music on your iPhone, iPad, iPod touch, Mac, or PC - Apple Support and Listen to music and more in the Apple Music app - Apple Support