How to make Soap and a Hot Shower on a Desert Island

How do you make soap and a hot shower on a desert island? In "Red Sand", survivors stuck on a desert island struggle with natives, sand fleas, a mysterious killer, and certainly hygiene issues. The mechanics of a hot shower would have slowed down the plot, but if you read it wondering, "How did they stay clean?", here's the answer.
Surrounded by stinky castaways? You're not the first. Among the travails of marooned mariners, hygiene typically gets the short shrift. It's hard for us modern folk to focus on famine, disease, and elemental exposure when the guy next to you stinks to high hell.
Luckily, even the rudest island has all the ingredients necessary to take a hot shower with real soap.
The following recipe