Okay, I found the Storage Usage settings, and went through all of the items.
I guess I had far more photos than I thought. Deleted most of them because they were mostly junk.
Found a few apps that were not very large by themselves but for some reason had accumulated a lot of storage. I deleted these too.
Even after all of this, it shows 11.56 GB used and only 1.24 GB free. I don't have very many apps on the phone, so I assume this is mostly used by iOS. Does this sound reasonable?
Also, there are a bunch of photos that I can't delete for some reason. These are photos that were not taken with the built-in camera, but were downloaded from my Mac one time when it was synched. Any idea how to delete these?