I unpacked the tar file of the 2.12.2 distribution into the directory where I had 2.12.1. Then, I logged into the back end, as Luisehahne suggested, as admin (user ID 1). This gave me a button to press to start the upgrade.
I selected options (in this case, show upgrade details and confirm back up options), and clicked the "Start upgrade script" button. It finished without any evident error. I got an error when I went to the front end, but that's because I've added some functions and they were not represented in the new files. I added those and the front end came up.
I was able to add a new user without getting an error, which was the reason I originally went through this upgrade. I have a number of other issues, but I'll put them in their own messages.