1) Do you have an iPod touch ?
The Spotify iPhone app will work on the iPod touch in the same way that it does on the iPhone. Of course, internet access is only over wi-fi, so the best way to use your iPod touch is to sync up some playlists for offline use when you have an available wi-fi network, and then you're good to go.
If you are unlucky enough to encounter a problem, and your can't find a solution in the FAQ, it's best not to look for help this board. Head over to the Spotify Community's iOS Board instead.
The rest of the points below don't apply to iPod touch users.
2) No subscription required
Everybody can use Spotify to sync their music to an iPod. You already own the music that you sync to an iPod.
3) Only local files can be synced to an iPod
Spotify isn't just about streaming. It is also a local media player. Spotify aims to gather together all your music in one place, so that you can combine Spotify's online catalogue with music files that you already own. Syncing of local music files to your iPod is one of the media player functions that Spotify offers.
Spotify's streaming music can't be synced to your iPod. There is a good reason for this. It is the same reason that you can't burn streaming music to CD, or save it permanently on your computer.
Spotify supports the music industry by passing on the majority of its income (from ads and subscriptions) to the rights holders who are responsible for creating the music. Rights holders are paid in relation to how much their music is played. Even offline plays are recorded when you go back online again.
This system can only work when there is a Spotify app to manage the music, keeping it "in the system". The iPod doesn't support any apps. So, if it were possible to sync streaming music to an iPod, this would mean that the people who created the music wouldn't get any further income when it is enjoyed.
4) Make sure that you back-up !
When you sync your iPod with Spotify for the first time, any existing content has to be erased, so be sure to backup your music via iTunes before syncing.
5) The iPod FAQ