In 1959, shy Todd Anderson (Ethan Hawke) begins his senior year of high school at Welton Academy, an elite prep boarding school. He is assigned one of Welton's most promising students, Neil Perry (Robert Sean Leonard), as his roommate and is quickly accepted by Neil's friends: romantic Knox Overstreet (Josh Charles), overachiever Richard Cameron (Dylan Kussman), best friends Steven Meeks (Allelon Ruggiero) and Gerard Pitts (James Waterston), and mischievous beatnik Charlie Dalton (Gale Hansen).
On the first day of classes, they are surprised by the unorthodox teaching methods of their new English teacher, John Keating (Robin Williams), a Welton alumnus who encourages his students to "make your lives extraordinary", a sentiment he summarizes with the Latin expression carpe diem ("seize the day"). His subsequent lessons include standing on his desk to teach the boys how they must look at life in a different way, telling them to rip out the introduction of their poetry books which explains a mathematical formula used for rating poetry, and inviting them to make up their own style of walking in a courtyard to encourage them to be individuals. His methods attract the suspicious attention of the strict Headmaster, Gale Nolan (Norman Lloyd).
Upon learning that Keating was a member of the unsanctioned group the Dead Poets' Society while he was at Welton, Neil restarts the club and he and his friends sneak off campus at night to a cave where they read poetry and verse, including their own compositions. As the school year progresses, Keating's lessons and their involvement with the club encourage them to live their lives on their own terms. Knox pursues Chris Noel, a girl who is dating a football player and whose family is friends with his. Neil discovers his love of acting and gets the lead in a local production of A Midsummer Night's Dream, despite the fact that his domineering father (Kurtwood Smith) wants him to go to medical school. Keating also helps Todd come out of his shell and realize his potential when he takes him through an exercise in self-expression, resulting in his composing a poem spontaneously in front of the class.
Charlie, however, takes the inspiration and Keating's teachings too far, publishing an article in the school newspaper in the name of the Dead Poets Society which demands that girls be admitted to Welton. Nolan uses corporal punishment to force Charlie to tell him who else is in the Dead Poets Society, but he refuses. Nolan also speaks to Keating, warning him that he should discourage his students from questioning authority.
Neil's father discovers Neil's involvement in the play and tells him to quit on the eve of the opening performance. Devastated, Neil goes to Keating, who advises him to stand his ground and prove to his father that his love of acting is something he takes seriously. When Keating asks the next day if Neil has spoken to his father, Neil lies and says that his father will let him pursue an acting career provided that he keeps up with his schoolwork. He discovers he is wrong when his father unexpectedly shows up at the performance. He takes him home and tells him he is forcing him into military school so he can eventually go to Harvard University. Lacking the courage to stand up to his father, Neil commits suicide by secretly stealing his father's gun and shooting himself in the head.
Nolan begins an investigation into Neil's death, at the request of the Perry family. Cameron goes to him, blames Neil's death on Keating to escape punishment for his own participation in the Dead Poets Society, and names Knox, Meeks, Pitts, Todd, Neil and Charlie as the other members. Later, confronted by Charlie, Cameron urges the rest of them to let Keating take the fall. Charlie punches Cameron and is later expelled. Each of the boys is called to Nolan's office to sign a letter attesting to the truth of Cameron's allegations, even though they know they are false. When Todd's turn comes, he initially is reluctant to sign, but seeing that the others have complied, does so.
Keating is fired and Nolan takes over teaching the class. Keating interrupts the class to collect some personal articles, but before he leaves Todd shouts that all of them were forced to sign the letter that resulted in his dismissal and that Neil's death wasn't his fault. Nolan makes Keating leave, but before he can do so Todd stands on his desk and salutes Keating with the words "O Captain! My Captain!". Knox, Meeks, Pitts and over half the rest of the class does the same, despite Nolan's threats to expel them. Deeply touched by their gesture, Keating thanks the boys.