Part 1. Official Way to Play Spotify Music on Galaxy S8/S9
Download Spotify Songs Offline
The Spotify app is only available on some countries and it may not be available if you travel around. Good news is that Spotify Premium users are allowed to download music for offline listening. If you are a new Spotify Premium user, you can simply setup the app to download the songs.
Step 1. You can login the Spotify website on your Galaxy S9/S8 to install the program directly or you can go to the Google Play store.
Step 2. When it is installed completely, you can double click the app to launch it and search the songs you want to listen to.
Step 3. To cache the files, you just need to switch on the "Download" icon to the right of an album, playlist, podcasts, songs.
Step 4. Your files will start to download. When it is done, you will see the "Downloaded symbol" finally.
Sync Spotify from Computer
On the other hand, if you have already backed up your Spotify songs on your Windows/Mac computer, it is better to sync the music from your Mac/Windows to the Galaxy mobile phone.
Step 1. Connect your Samsung Galaxy S9 to the computer via an USB cable. It should show up under the "Devices" tab on the Spotify of your computer.
Step 2. Right click to select your phone and choose "Sync 'your device's name' with Spotify".
Step 3. It will show you all the playlists from Spotify which are available for transferring. You can choose to sync all the songs automatically or select the special songs you like to transfer manually.

Note: The above two ways require you to subscribe Spotify Premium membership to do that. If you only have a free account, then you will only be able to stream music online randomly.