How should one water an African violet?
I bought it from Franks, and it came in a plastic container with no holes
in the bottom.

Unbelievable. Are you sure it isn't in a pot inside a cachepot? If it otherwise
doesn't need repotting, see if you can make holes in the bottom with a
soldering iron or a sharp tool.
I water African violets by putting the spout of the watering can between the
leaves.
Iris,
Central NY, Zone 5a, Sunset Zone 40
"If we see light at the end of the tunnel, It's the light of the oncoming
train."
Robert Lowell (1917-1977)