So I wanted to integrate the spotify library into an android app. I went to https://developer.spotify.com/technologies/libspotify/ and downloaded their lib libspotify-12.1.5
Unfortunately, Spotify doesn't have a nice Java library for Android (see this StackOverflow question for more details), so you'll have to manually write a JNI wrapper. As the Android build of libspotify is pretty new, there aren't yet any examples for that either, but I wouldn't be surprised to see the documentation include them soon.
As @juned noted in his comment, this question details how to get the libspotify libraries linked with your Android app. Once you get libspotify linked correctly, you can check out a few Android NDK tutorials for more specific integration help.
If you have troubles during your integration, be sure to check out the example code which Spotify ships with libspotify. The code provides a good reference of how to properly talk with the Spotify service with the library.