Given the broad nature of this question, I will only be able to give you a rough summary of the novel. I have included links below to the enotes study sections based on this novel that you can access to find out more information.
The novel is told from the perspective of Bud Caldwell, who, as the novel opens, decides to run away from an orphanage and a foster home where he is treated cruelly. The novel is set in the 1930s, and thus the Great Depression is in full swing. As Bud Caldwell sets off to try and find his father, the only clue he has as to the identity of this figure is a blue flyer advertising a jazz band. He carried this flyer and a few other belongings that were his mother's in a suitcase.
Bud's quest places him in contact with a wide range of different kinds of people set against the backdrop of general want and poverty. However, he finally manages to reach Grand Calloway Station and to meet the person that he concludes must be his father. As he journeys, Bud in many ways seeks to discover his own identity and a home, and when he reaches his destination, he discovers that he has found both, though not in ways that he expected.