Sent my I-129F off to the Vermont Service Center on December 20, and received my return receipt indicating that they received it on December 27. Now what?

Don

Now you wait for NOA 1 (that's indicating they opened the petition/started to process it, you should receive that pretty much every day now) and for NOA 2 (the actual petition approval, that will take a couple of weeks/months, depending on the current processing times).
Check the K1 guide http://www.visajourney.com/forums/index.ph...mp;page=k1guide
and the K1 flowchart http://www.visajourney.com/forums/index.ph...amp;page=k1flow
for detailed infos on what's going to happen next, how long it will take appr. and what you can do to start preparing yourself and your fianceé for the embassy process overseas in her home country.

Yep read the guides