The rising action of the plot is what happens after the exposition as the key conflict slowly but surely develops, leading to its ultimate expression, which is the climax of the tale. If we see the conflict in this book as being Sal and Dean vs. society but also the relationship of Sal and Dean, there are a number of important moments that form the rising action and lead up to the conflict.
1) Sal on his first trip hitchhiking west and what he learns about himself. He also sees Dean trying to balance his wife and a girlfriend.
2) Sal's time in San Fransisco and his job as a special policeman and then his relationship with Terry.
3) Christmas when Sal meets up with Dean again in Virginia and they go on another road trip. Sal finds Dean's craziness too much and he leaves for New York.
4) Sal and Dean go to New York after a week of drinking and stealing in Denver. Then Dean later joins Sal on another road trip as he can't resist the temptation of journeying again.
5) Their experience in Mexico is another key moment as they experience both the simplicity and chaotic sides of Mexican life.
This of course leads to the climax of the story, which is when Dean abandons Sal at his time of need in Mexico City.