The story ends with a misinterpretation. How has the author prepared us to understand simultaneously how the doctor might arrive at this conclusion and how this conclusion is wrong?

First, the misinterpretation: the doctor concludes that Louise's death was precipitated by a grave shock. Since Louise suffers from a heart condition, this interpretation is only natural.
However, the author does prepare us to understand how the doctor arrives at this conclusion. She begins the first line of the story with pointed information: Mrs. Mallard has "heart trouble," so she must not receive sudden shocks. Any bad news must be broken to her gently.
The author also prepares us to understand how the doctor's conclusion is wrong. After Louise retires to her room, Chopin introduces the idea of a foreign emotion holding Louise in its grip. Until she entered her room, Louise had only shown one emotion: unrestrained grief. Now, a separate emotion threatens her composure.

There was something coming to her and she was waiting for it, fearfully. What was it? She did not know; it was too subtle and elusive to name. But she felt it, creeping out of the sky, reaching toward her through the sounds, the scents, the color that filled the air. Now her bosom rose and fell tumultuously. She was beginning to recognize this thing that was approaching to possess her, and she was striving to beat it back with her will—as powerless as her two white slender hands would have been.

At first, the emotion is "too subtle" to name. When Louise finally recognizes it for what it is, she tries to reject it. However, Chopin tells us that she is powerless to do so. In fact, the repetitively murmured "free, free, free" alerts us to Louise's frank, unadorned glee. We suddenly realize that Louise is actually looking forward to life away from the shadow of a "powerful will."
This sense of freedom is an "elixir of life" to Louise. The first moments of sheer grief have given way to a pragmatic assessment of her situation. The doctor, however, is not privy to Louise's private "feverish triumph" over her initial emotions. Because of his knowledge of Louise's heart condition, he misinterprets her cause of death.