Make sure your device is up to date then go to the app store and download Spotify. You should be able to use the app once downloaded. Spotify doesn't support iOS 4. And as it is possible to downgrade iOS, it's a hefty process.
"Spotify supports streaming and offline syncing to iPod touch versions with iOS 5 or later. You can sync only your local files to the following models: All iPod classic, nano shuffle, except the very early Firewire versions." - x
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