If you're using the latest version of the app (version 8.6), there's a new feature that lets you download songs for offline listening on your phone or tablet.

To enable this, open Spotify then go to Settings > Offline mode > Download files when idle > Select Yes (to download) or No (if you change your mind).

You'll be able to see downloaded tracks in their own section under Library in the left sidebar menu on Spotify Web Player or in My Music after you've logged into your account on the Spotify Music app.

To download a song, simply tap the three dots next to it and hit download button.

The song will be available offline in offline mode so you can listen to it anytime even when there is no internet connection.