Von, thanks for your information.  I've put a picture on this post.  Not sure if it has a packing nut or not.  I couldn't figure out how to draw an arrow on my photo editing program so I drew a green line.  That part where the water comes out is where it's leaking.  The red and blue handles are there, and further up is where the shutoff valves are.  To the right is the washer and dryer.

I can see the point about the plumbing thing, but my expectations have definitely NOT been managed ahead of time.

On my way to take my garbage over to my friend's house (for those who don't know, we split the cost of garbage and I take my garbage over and put it in her can), I ran into the guy down the street who's a plumber.  He said he'd take a look at it after work (side job).  He mentioned the term "packing nut" too.

(Under Laundry Sink.JPG)

Under Laundry Sink.JPG (32KB - 89 downloads)