"The Yellow Wallpaper" discussion what might a psychoanalytical reading of Gilman's story focus upon? What elements would be focused on in a formalist reading of the same text? .

A psychoanalytical reading of "The Yellow Wallpaper" could focus on the narrator's incipient mental illness.  She could be viewed as suffering from postpartum depression after the birth of her child, or perhaps psychosis, as she sees a woman trapped in the wallpaper and works to free her.  Alternatively, a psychoanalytic reading could focus on Charlotte Perkins Gilman, the author, the unhappiness she felt in her own marriage, and her feelings about feminism and paternalism in the lives of women. 
Formalist readings do not take into account anything external to the text.  A formalist reading of the story would focus on its structure:  how the narrative is organized, its tone, imagery, and style.  A formalist reading of "The Yellow Wallpaper" would focus on the first-person narration, the reliability of the narrator, how the word choices create the story's tone, symbolism, and the development of the plot.