How is irony used in this story? How is the wallpaper used as a symbol for the life of the narrator? Responding requires active mental engagement: exploring ideas, forming conclusions and, ultimately, critiquing, as objectively as possible, what you have read.

An assignment such as this requires you to think very carefully about what you pull away from the text and how you interpret its meaning. There are a variety of directions you can go with this kind of assignment: it will really come down to how you relate to the story in question.
That being said, before going into more detail, it will be useful to iron out something involving the terminology. An ironic situation is one where the outcome outcome runs contrary to one's expectations. A contemporary example of irony can be found in the backstory of Harry Potter, where Lord Voldemort learns of a Chosen One (Harry) prophesied to oppose him and attempts to murder Harry in his infancy. In trying to prevent the prophecy from coming to fruition, however, Voldemort ends up triggering it instead.
Of course, you won't find any self-fulfilling prophesies in "The Yellow Wallpaper" (these are largely limited to fantasy or mythic literature), but there is irony within this story all the same. In this case, if you wish to address the topic of irony, think about the characters within the story, think about their actions, and particularly think in terms of the intentions behind their actions. Weigh those intentions against the outcomes which result from them.
Additionally, I'd suggest you think carefully in terms of the characterization. What do you know about the story's protagonist? What is she going through? What relationships does she have with other people, and how are those relationships themselves portrayed? "The Yellow Wallpaper" is often understood as containing within it a very powerful critique of gender expectations as they were understood in the nineteenth century. How is that criticism expressed within the story itself?
Furthermore, can you tie various literary devices together—characterization, themes, the use of symbolism, the use of language, the use of irony? Stories tend to be multifaceted, after all, so various literary devices are interwoven. Seeking out how these different aspects are interconnected with each other can be just as rewarding as looking at them in isolation.