Please see the link below to Apple's Support Site for instructions on moving content from Apple Music on your computer to your devices:
Add content from Apple Music
- Connect your device to your computer.
- Open Apple Music. Make sure that you have the latest version.
- Select the content that you want to add to your device from your iTunes library.
- Look in the left sidebar for your device, then drag the content to your iPhone, iPad, or iPod touch.