A Fistful of Fig Newtons follows Ralph Parker on a long trip through the Lincoln Tunnel from New York to New Jersey. As Ralph sits in the tunnel, stuck in traffic, he reminisces over scenes of his life and speculates about the future and the state of culture. The reader travels with Ralph through memories of his childhood, the army, and life in college on the GI Bill.

As the story begins, the narrator is just approaching the Lincoln Tunnel in stand-still traffic. As he gets inside the tunnel, his mind begins to wander. First, he recalls an episode while he is in college on the GI Bill. His Fig Newtons attract three dorm-mates to his room, and Big Al, a football star, begins arguing with erudite anti-athlete Umbaugh. Umbaugh challenges the others to a chocolate laxative-eating contest, which his opponents lose. The narrator runs for the restroom, while Big Al winds up collapsed on the floor, unable to move. He can't play in the next day's big game, and the college loses.

Then, the narrator ruminates what a strange place New Jersey is, the light at the end of his tunnel. His thoughts are brought back again to his past, and he remembers his first summer at camp. As a first-year camper, he was picked on by the older boys and forced into menial duties like cleaning up trash (foreshadowing his future army career). A boy named Skunk, who no one talks to, surprisingly wins the camp treasure hunt for the narrator's lodge.

The narrator recalls being trapped between a tailgater and a truck full of crushed cars, thinking of how his mind wanders creatively while driving. While trapped, he thinks up stories about the crushed cars. Then, he remembers moving out with his army troop. After a grueling KP duty, one of this company members gets off the train to get beers, and the train starts up and leaves without him. The narrator's mind wanders again, comparing Van Culture to Camper Culture in a made-up sociology lecture.

The narrator then mentions writing an article for a car company magazine. The article describes a conversation with an ad executive who works for a lemon counsel. He describes the difficulty of promoting lemons, chickens, and other things used disparagingly in common language. The narrator's mind flashes forward to the future. He imagines future archaeologists digging up New York and their impressions of the culture based on TV commercials.

After discussing a catalog of oddities, the narrator reminiscences about his grammar school, where he learned nothing because he was always stuck in the back of the class. He miraculously passes algebra with a flash of luck or inspiration in deciphering an equation at the board. The narrator recalls another childhood event, an ice cream price war in his home town, resulting in the local ice cream parlor running the big chain ice cream store out of business. Finally, he remembers coming come after being let out of the army, and in this memory, his name, Ralph Parker, is revealed. Ralph goes out on the town for his first New Year's as a free man, and his date with a reverend's daughter turns into a disaster when she drags him into a bar and proceeds to get drunk and pass out. Still, Ralph is a free man, and he finally exits the Lincoln Tunnel.