If you have version 1.0.1 of the Spotify desktop app:
The devices section will be coming back in a future update.
In the meantime:
You won't be able to see an indication in the desktop client that the device is paired with the desktop client. But as long as they both are on the same WiFi network you should be able to trigger the local files sync by toggling the offline toggle on the playlist on your phone. Just make sure all your local files are in the playlist you switch to offline in the desktop app.
MattSudaRock Star 24
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I'm having the same problem with my BRAND NEW nano. I have only begun using spotify a few days ago and I do not have itunes on my computer. I pretty much down right to refuse to use itunes at all costs. I have premuim spotify and wanted to being syncing songs. Now I'm no computer idoit however I cannot seem to even get spotify to recognize my nano. Help.