If Spotify isn’t showing up in your preferred app store, it’s likely that you’re in a country where the service isn’t available. Don’t be tempted to grab the APK file directly from a third-party website; there’s no telling whether the app you’re installing is actually Spotify, or even if it’s safe. Besides, the Spotify app checks your IP address to make sure you’re in a supported country, so even if you manage to install it, you’ll still need a VPN before you can listen to anything.
Here’s the solution: just connect to a VPN server in one of Spotify’s supported locations. This should change the apps available in your app store and allow you to use the service as normal from anywhere in the world.