I'm not a big fan of linking my geocaching.com account with either my Facebook account nor my Twitter account, and have opted not to do so. I don't see the benefits. If you you'd like to give it a try, you'll find the appropriate settings on your geocaching.com account details page. Look for the Facebook and Twitter icons.
But one connection between FB and GC.com that I do enjoy is how people in our East Bay Geocaching Group can post Events using Facebook's Events feature. This Picnic Event Cache was posted on Facebook, and gives us cachers the opportunity to RSVP via Facebook:
Of course you'd still have to go to the cache page on gc.com
if you want to post a "will attend" note, but at least Facebook gives
local cachers another RSVP option, and more importantly, a means of
notifying cachers of local events that we might otherwise miss on the