If you want to publish your runs collected in garmin connect to facebook there are two ways:
- Using the garmin connect rss feed (has to be public) and a service like http://dlvr.it/ to add any new run to facebook.
- On the other hand http://runkeeper.com and http://www.garminsync.com/ plugin can be used to sync from garmin connect to runkeeper and from there to facebook.
I had problems with the garmin connect rss feed so I tried second approach. And there is also an bulk import to import old activites to run keeper. But this is running for ages if you have many activities but still it works.