We're having a bit of a drought around here, so water conservation is the order
of the day. Leaving the tap running is kinda wasteful.

I fill the basin about 3/4 full, soak a hand towel and use it to wet my face.
Then I fold the towel in half lengthwise, roll it up, and place it in the water.
During the shave, I wipe the razor on the nearly submerged towel.

At the end of the shave I give the towel a bit of a squeeze and use it to
wipe off my face. Then drain the sink, rinse the towel, wipe my face again,
and then the razor.

Finish by wiping the razor off on a dry towel and then dry my face.

The wet towel gets a final quick rinse, then wring it out and hang it up to dry,
until the next shave.