To draw a timeline based on events in Avi's The Man Who Was Poe, you first need to identify the setting of the story, in terms of dates and hours, as best you can.
We can deduce that the story is set in the year 1848 and takes place at least a few days before the election declaring Zachary Taylor to be the 16th President of the United States. We learn this based on a few details. First, a few notices posted in the salon and in the newspaper provide important clues about the setting. One of the notices was written by Edmund's Aunt Pru and is dated October 15, 1848. The notice advertises a monetary award for anyone who can provide information leading to the whereabouts of her sister, who is Edmund's mother. Based on the details of the story, we know Aunt Pru posted the notice soon after arriving in Providence, Rhode Island. Another notice is read by Poe in the newspaper and advertises the services of Frank Foster as a game and oyster caterer, especially for parties taking place near the US Presidential Election, which at the time took place on November 8th. Edmund also informs Poe that he and his family have been in America for almost a month. If they arrived near October 15th, then we know the story occurs only a few days before the election, though we don't know exactly which day. Since the story doesn't end on election day, we can guess that the final events of the story take place November 7th.
If we continue tracing the story, we know that Edmund and Poe are together for one full day and two nights; Sis is rescued at dawn on the final day, which I am guessing is November 7th. This tells us your timeline should start on November 5th. You will mark most events as occurring on November 6th; therefore, it may also help you to learn the hours at which the events occur. There are two important time references within the story: 11 am, which is the time the inquest investigating Aunt Pru's murder takes place, and 3:30 pm, which is when Poe is expected to be at Mrs. Whitman's for the tea party. Additionally, on November 7th, Edmund heads to the docks to rescue his sister at about 6 am.
After you have drawn your timeline and marked the important dates and hours, you're ready to decide which events to put on your timeline. You want to choose your events based on the important elements of plot, which are always the exposition, rising action, climax, falling action, and resolution.
Authors use exposition to set the story, introduce the characters, and point out the conflict. Some of the most important moments of the exposition are when Sis goes missing, since this is the conflict, and when Edmund meets Poe, since this meeting drives the rest of the story.
The term rising action refers to all events leading up to the story's climax, which is the turning point of the story. The story begins to turn the moment Edmund realizes that, though Poe solved the mystery, Edmund is on his own to actually rescue his sister. All events leading to Poe solving the mystery count as rising action. All of the events that take place at the docks and on board the Peggy as Edmund, Throck, and Poe chase after Sis's kidnappers count as falling action, which are events leading up to the story's resolution. The resolution is, of course, not only the moment Edmund successfully rescues Sis but also the moment Edmund learns exactly what Poe's motives for solving the mystery had been throughout the story and why.