The exposition is the introduction, where the author gives the reader background information about the characters and the plot. This story is told as a flashback. Bill tells the reader about the idea they had to kidnap a child to get some money.
The conflict is created not by the kidnapping, but by the kid they took.
"From this time on, Johnny is in power, annoying his captors with chatter and questions, keeping them from sleeping, terrifying Bill with an attempted scalping at daybreak—followed by an attack with a hot potato and later with a rock—and generally enjoying himself so much that he seems disinclined to return home."
Internal conflict comes in the form of doubts that the kidnappers have over the choice they made. The external conflicts are many between the boy, and his captors as listed above. And between the two captors, who will look after Johnny.
The climax, the ransom note. Falling action, Johnny's Dad refuses to pay to get his son back, but instead tells them:
"You bring Johnny home and pay me two hundred and fifty dollars in cash, and I agree to take him off your hands." (O'Henry)
The resolution is not easy for the captors, Johnny does not want to go home. They have to trick him into going home.
"they must run at top speed to escape the boy who does not wish to lose his new playmates, the would-be kidnappers who have become his victims." (O. Henry)