It bills itself as a "Cinderella story," but I'm not really sure what parallels can be drawn between this story and Cinderella apart from the main character being a girl who has two vain sisters who make her tend the fire and lie to the local bigwig in an attempt to marry him. There's no fairy godmother, no glass slipper, no fancy ball, and no midnight change. The author's notes say it's from an Algonquin tale.
There's a village of wigwams, probably an Algonquin village. In this village, there's a super awesome big tent, inside of which lives the Invisible Being. Everybody wants to marry him, although it's never really explained why. Presumably he is rich? He doesn't seem to be in charge of the village, since he doesn't actually communicate with the villagers other than through his visible sister. The book says he's "very great, rich, powerful, supposedly handsome." His sister can see him, although nobody else can. She says, "Only the one who can see him can marry him."
There's a poor man in the village who has three daughters. The two older daughters are nasty and mean and they make the younger daughter tend the fire all the time so her face, arms, and hands get scarred by cinders, hence the name "The Rough Face Girl." They tell their father to give them expensive clothes so they can go marry the Invisible Being. They walk through the village, all haughty, to the wigwam of the Invisible Being. His sister asks, "Why have you come?" They say, "We want to marry the Invisible Being." So she says that they need to have seen him. She asks what his bow is made of, and they say "The great oak tree." She says no. She asks what the runner of his sled is made from. They say, "The green willow branch." She says, no, they haven't seen him. The girls say, 'Just test us.' So she sits them in the wigwam and they hear someone enter and a bow and a beaded quiver of arrows float in the air and they freak out. Ashamed, they go home.
The next day, the younger sister asks her father to give her some pretty things, but he doesn't have any money left after spending it on her sisters. He offers her his moccassins and some birch bark and other various seemingly useless items, which she dresses herself in and walks through the village, to the amusement of the villagers. But she has faith in herself. As she said to her father, "I am going to marry the Invisible Being, for, wherever I look, I see his face." She goes through the wilderness and wanders to the lake for some reason, instead of going to the Invisible Being's wigwam. The natural world is very beautiful, and she sees the Invisible Being in the sky and everywhere else. His sister is on the shore of the lake. She looks at the Rough Face Girl, and realizes that she is beautiful inside. RFG answers the sister's questions correctly: his bow is "the great curve of the Rainbow" ("AHHH!" says the sister), and the runner of his sled is the "Spirit Road, the Milky Way of stars that spreads across the sky." So the sister knows that RFG has seen him, and they go to his wigwam and he comes in and says she is so beautiful, and the sister gives her some awesome clothes and tells her to bathe in the lake. All the scars vanish from her so she is beautiful on the outside as well. She marries the Invisible Being and "They live together in great gladness and were never parted."
So it's the standard 'older siblings mean to younger sibling, younger sibling wins in the end' story that's all over the world, like Cinderella from Europe or Mufaro's Beautiful Daughters from Africa. It's unclear why RFG's father lets her sisters treat her so terribly. And in Mufaro's Beautiful Daughters, at least the younger daughter gets tested on her personality, and not her weird ability to see invisible things. As usual, the younger girl gets rewarded by marrying the best guy because that's what girls want.