I got it set up per Joe Rossignol’s screenshots, and once Apple Music is set as the default music source, it works really well. I could play music from my library, but the Echo could not find any of my personal playlists. Likewise, it could not play music that I had uploaded to iTunes Match.
I don’t know if these features will be available after the service’s official launch date, but as of right now, Apple Music on the Echo feels half-baked.
Update: I’ve gotten a couple of emails from people saying playlists are working for them, so maybe some of this is just teething problems.