Unfortunately there are no shut-off valves for the showers, so we have to turn the water off for the whole house at the meter. Having done that, we can proceed to take the faucets apart.
The Hot/Cold buttons just pry off. Then there is a screw that holds the handles on. Then a chrome extension that just slides off. And the escutcheons screw off. Have to be careful not to scrap the chrome off. Luckily we have a bathroom counter that we can lay the pieces out on as they come off.
Now there is a flange of some kind that screws off. And then the handle itself.
At the end of the handle is a washer, held on by a screw. This is what we want to replace. We went to Home Depot and got 3/8L flat washers (11/16" O.D.). The new ones do not seem as thick as the old one. And we got some new #10-24 brass round head machine screws to replace the hot water screw. It was thickly covered with sediment. The cold water screw looked in pristine shape, so we reused it.
Then we applied silicon plumber's seal to the inner most threads on the handles, and plumber's grease on the outer ones (which hold the escutcheons), and reassembled everything in the reverse order of taking it apart.
The result is a shower that does not drip. At least for now.
