You are Aldo Trapani. You are the son of one of the Corleones top men. When you are young your father is murdered by the Barzinis. Vito Corleone promises you that when you are old enough you can get revenge.
10 years later
You have fallen in with the wrong crowd and your mother asks the godfather for him to help you out. He agrees. You are now on your way working for the Corleone Family.
The rest of the plot is based on the original film. There is another thread of plot which has been created by Mike Winegardner specifically for the game. It includes the characters of Aldo Trapani, Johnny Trapani (his father), Monk Malone (his friend) and Frances Malone (sister of Monk and girlfriend of Aldo).
One of the goals of the game is to advance in rank in the Corleone Family and become Don of NYC.