There are a few examples of similes and metaphors in this story. I have provided three such examples below, with some brief explanation of each. I hope you find the examples and explanations useful.
She danced wildly, with passion, drunk on pleasure, forgetting everything in the triumph of her beauty, in the glory of her success, in a sort of cloud of happiness, made up of all this respect, all this admiration
In this first quotation, Mathilde is described as being "in a sort of cloud of happiness." This is a metaphor because, of course, she is not literally in a cloud. The metaphor helps to show how Mathilde, at this moment in the story, is surrounded by her own happiness, much as one would be surrounded by a cloud if one were in it. The cloud image also connotes that Mathilde is so happy that she feels like she is floating.
At the end of one week they had lost all hope. And Loisel . . . had aged five years
In this second quotation, the metaphor is, "Loisel ... had aged five years." Loisel hasn't literally aged five years in one week, but this metaphor suggests how stressful that one week was, by suggesting that Loisel's physical appearance has ben so drastically affected by it.
And, dressed like a commoner, she went to the fruiterer's, the grocer's, the butcher's, her basket on her arm, bargaining, insulted, fighting over every miserable sou.
In this third quotation the simile is, "dressed like a commoner." Comparing Mathilde's clothes to those of a commoner helps to emphasize how much poorer Mathilde has become, and how that poverty is now reflected in her physical appearance. The simile also helps to explain why Madame Forestier doesn't recognize her later in the story.