It's hard to really show with pictures how loose the faucet was, but here's my attempt:
I checked under the sink to see what kind of loose bolt I was dealing with and it was a thin hexagonal bolt so I got my adjustable wrench from my trusty toolbox. A few quick righty tighties underneath my cramped sink and that sucker was nice and sturdy once again. While I was at it, I cleaned out the sink using this method because it was dirrrrrrty.
I also tightened up all of the legs on the kitchen table. One leg was particularly loose and it turns out there's a stinkin' crack in the leg!
After a couple of righty tighties, with my woefully underused Allen keys, and things were lookin' good once again.