For a while now, the Google Play Music app has had the ability to download tracks to microSD cards for offline listening. You'll need an Android smartphone or tablet with a microSD card slot and a microSD card with some free space. The feature has been designed for Android 4.4 KitKat but Google said it is available for some older devices in 'experimental form'. So it's worth trying if you have an older device but you may experience problems.
There is an iOS app for Google Music but Apple doesn't offer expandable storage on the iPhone or iPad so this guide doesn't apply. See also: Spotify vs Google Music comparison review.
How to get Google Music to download to SD card
Step OneOpen the Google Play Music app on your device.
Download Music