How do I sync my Zwift data with TrainingPeaks, Garmin Connect, etc.?

As of mid-January 2016, this wasn't an enabled feature (it was marked as "Planned" by the Zwift Engineering team for awhile), but Zwift quickly enabled it and added direct support for synchronizing your Zwift activities with TrainingPeaks as well as Strava!

If you want to use the Strava → Garmin Connect → TrainingPeaks method to get your data to any of those three services, there's a very detailed HOWTO on TriNut (a site dedicated to triathletes) describing each of the steps you'll need. 

If that seems a bit complex or confusing, you could also try using "tapiriik" to sync your data between these (and many other) services. Some have reported great success, while others have reported issues. Give it a try and see if it works for you!