Spotify desktop users have had the ability to enable private listening for about a month now. Spotify just recently updated its Android app to include the feature for Android users as well. Here's how to enable it:
Step 2: Launch the Spotify for Android app, then in the lower right-hand corner, tap on "More," then "Settings."
Step 3: Check the box next to "Private Session."
Step 4: When you go back to your playlists, you'll see the "Private Session" indicator at the top.
That's it. Now you can listen to Spotify without advertising your playlists to your Facebook friends. Keep in mind that after 6 hours of idle time, Private Session will automatically disable itself. To permanently disable Facebook integration, read this post by Matt Elliot.