I turned off the computer, turned the keyboard over to get most of the water out and dried off the keytops with a towel, then left the keyboard upside-down to dry out more.
In the evening, Stella suggested taking the keytops off to get any remaining water out. It's amazing how much cruft has accumulated there; mostly hairs of mine; she also dusted must of that off with a brush. She also took the cover of the keyboard off so that she could dust better, and put the keycaps into a boal with warm water and some dishwashing liquid to soften some of the gunk and oil that has accumulated over the months.
Today she said she'd vacuum the keyboard and also rinse and dry the keycaps. So hopefully my keyboard will be back in service again tonight.