In the Introduction to My Antonia, what has Jim been doing to amuse himself on his long trips across the country?
There are two introductions, one published in 1933, the other in the earlier edition, 1918. I assume you refer to the more common and recent introduction, although current editions include both. In the more recent introduction, the “I,” or author, says she and Jim sit in the observation car “talking about what it is like to spend one’s childhood in little towns” like those they pass as the train goes through Nebraska. Significantly, she also reminds us that Jim has the “same romantic disposition which made him very funny as a boy.” This statement is key to everything that follows because it suggests that what he says might be slightly overwrought and idealized both in relation to the countryside but also in relation to all he says about Antonia in the chapters that follow. In other words, this comment of the “I” in the introduction cautions us that Jim is not a fully reliable narrator of the life of Antonia. And so, what he is doing to amuse himself is "romanticize" about his life in Nebraska when he was a child rather than remember the events as they occurred.
Jim "loves with a personal passion the great country through which his railway runs and branches", so he likes to sit in the observation car watching the scenery flash by. The little towns that he sees reminds him of "what it is like to spend one's childhood" in such places, and in the introduction, he and the author, who grew up with Jim, are talking about these remembrances, and in particular, Antonia, a Bohemian girl they once knew. More than anyone else, Antonia "seemed to mean to (them) the country, the conditions, the whole adventure of (their) childhood", and Jim and the author wonder why they never wrote about her.
A few months after this encounter, Jim gives the author a manuscript which he has written about Antonia. This manuscript, "substantially as he brought it", became the book My Antonia.
(all quotes from "Author's Introduction" in My Antonia)