"You never really understand a person until you consider things from his point of view - until you climb into his skin and walk around in it"
How does atticus' statement help scout negotiate and understand the events of the novel to kill a mockingbird
Scout is not aware of the importance of Atticus' advice until she stands on the Radley's porch at the very end of the novel. She doesn't respond to Walter Cunningham because she is seeing things from his perspective. She is utterly unaware of what she's doing, other than being polite to grown-ups, as her father has taught her. Similarly, she shows curiosity about Calpurnia's church, and First Purchase's style of worship, but she doesn't understand the difference between her church and Calpurnia's. She can't comprehend Miss Gates's comments about "those people." And she doesn't understand why Jem and Dill are so upset at the outcome of the trial.
The power of "To Kill a Mockingbird" is that the narrator reconstructs events from her childhood, from the perspective of an adult. At the time they are happening, Scout has no clue of their significance; to her, it is only the story of how Jem's arm was broken. Jem has the maturity to interpret what he sees. All Scout does is record.
So the short answer is that Atticus's statement is of no use to her at the time. It is only in retrospect that she can put together the pieces of the story and grasp how she has, unconsciously, been affected by Atticus's advice.
This advice helps Scout navigate the large and small events of the novel in the same way. Despite her pride and her temper, Atticus' advice gives her ways to slip past the prejudice all around her, to resist the anger and fear that define the community, and to identify with people that others find alien or inferior. It softens her heart, allowing her to defuse the mob scene facing down Atticus by the jail, and it allows her to realize that her perspective isn't the only one, as happens repeatedly through the novel (in Calpurnia's church, for example, or in watching the trial itself). It softens her emotion and opens her imagination, or better, gives her natural imagination a method for doing the right thing.
This important snippet of conversation from Chapter 3 finds Atticus giving Scout the crucial piece of moral advice that governs her development for the rest of the novel. The simple wisdom of Atticus’s words reflects the uncomplicated manner in which he guides himself by this sole principle. His ability to relate to his children is manifested in his restatement of this principle in terms that Scout can understand (“climb into his skin and walk around in it”). Scout struggles, with varying degrees of success, to put Atticus’s advice into practice and to live with sympathy and understanding toward others. At the end of the book, she succeeds in comprehending Boo Radley’s perspective, fulfilling Atticus’s advice in Chapter 3 and providing the novel with an optimistic ending despite the considerable darkness of the plot.