The previous posters have some good comments, but I want to add a little more information about formalist criticism. This sort of criticism is very attentive to the specific language -- the "local texture," as some New Critics call it -- of the literary work. Whether refering to Russian formalism or New Criticism, for example, the formalist theoretical approach pays close attention to the words and language patterns (e.g. sentence structures) used in the story.
What this approach does not focus on is just as important, of course. There should be little to no dicussion of the author, the historical context, or the reception of the work. (I would even recommend never asking the quastion "Why does Chopin...," as one poster recommends. Instead, a die-hard formalist is more likely to ask: "Why does the story...")
When using the formalist viewpoint, it helps to look more at how the story is written, rather than the content or ideas behind it, and how the structure of the writing and the plot itself contributes to the themes, not the other way around. Some questions to ask yourself about its structure might be, why is this story so short? Why does Chopin end it on quoted dialogue from the doctor as to the hypothetical reason that Louise died? Why does Chopin spend so much time describing the beautiful weather and distant song that she sees and hears outside of her window? Also, leave out historical background, or the author's intent, or any outside influences--just look at the actual text itself. If you take a look at all of these questions, it will help guide a criticism from a formalist viewpoint.
I'll tackle one of the proposed questions, as a way to get you started. For example, after Louise hears the news of her husband's death, she goes up to her room and looks out the window where she sees
"the tops of trees that were all aquiver with the new spring life. The delicious breath of rain was in the air. In the street below a peddler was crying his wares. The notes of a distant song which some one was singing reached her faintly, and countless sparrows were twittering in the eaves. There were patches of blue sky showing here and there through the clouds that had met and piled one above the other in the west facing her window."
Ask yourself--in such a short story, why does Chopin take up over an entire paragraph just describing the scene outside the window? Could it have relevance to the theme of the story? Here, Chopin is using symbolism and foreshadowing. The beautiful scene, the spring air, the leaves being full of new life, the song in the distance, all symbolize and foreshadow her coming sense of freedom and elation at not being bound by the ties of marriage anymore. It represented Louise's coming emotional state, and spoke of her feeling of happiness and freedom. Spending that time using foreshadowing contributed directly to the theme of the story itself.
I hope that gives you an idea of how to tackle some of the other elements of the plot. Good luck!
A formalist viewpoint is analysis of a work based only on its form, or content. Kate Chopin's "The Story of an Hour" is built up out of Louise’s conflicting roles of bereavement and liberation. Louise herself, the protagonist, feels identified with liberation, while all the others in the story assume the status of antagonists because they project upon her the role of grieving widow. The crisis and climax both occur almost simultaneously (in paragraph 21) when Brently Mallard enters the house and Louise falls dead of a heart attack upon seeing him. One might make a case that the climax has been already established by Brently’s having escaped the train crash, for it has been stated right at the beginning of the story that Louise’s heart is weak (paragraph 1), and therefore any sudden shock would kill her. The resolution is of course the reassertion of male dominance, as expressed by the doctors.