How do I my iTunes library on my iPhone

you can sync Use iTunes to sync your iPhone, iPad, or iPod with your computer - Apple Support

or you can listen to the computers shared itunes lib Use Home Sharing to share media from a computer to other devices - Apple Support

TGIII Said:

"How do I listen to my iTunes library on my iPhone? Thanks”

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Use the Music App or the TV App:

In recent iOS versions, there is no iTunes. So, use the Music app for Music, and use the TV app for TV Shows and Movies. Learn More Here:  What happened to iTunes - Apple Support