Spotify has landed on the Apple Watch, just update the app on your iPhone (v.8.4.79) and it should show up on the watch (unless youve disabled Automatic App Install). If you havent already, you can download Spotify from the App Store.
Note that this is just remote control for the music playback on your phone you can play/pause, skip tracks and fast forward/rewind. You can also use this to control Spotify Connect speakers (Connect was recently enabled on the free tier).
Spotify is working on a fully offline, phone-free experience, which will be a true alternative to Apple Music, but that’s apparently not ready yet.