It is 1868. Ethan Edwards (Wayne) returns after an eight-year absence to the home of his brother Aaron (Walter Coy) in the wilderness of West Texas. Ethan fought in the Civil War on the side of the Confederacy, and in the three years since that war ended he apparently fought in the Mexican revolutionary war as well. He has a large quantity of gold coins of uncertain origin in his possession, and a medal from the Mexican campaign that he gives to his eight-year-old niece, Debbie (played as a child by Lana Wood). As a former Confederate soldier, he is asked to take an oath of allegiance to the Texas Rangers; he refuses. As Rev. Captain Samuel Clayton (Ward Bond) remarks, Ethan "fits a lot of descriptions".
Shortly after Ethan's arrival, cattle belonging to his neighbor Lars Jorgensen (John Qualen) are stolen, and when Captain Clayton leads Ethan and a group of Rangers to recover them, they discover that the theft was a Comanche ploy to draw the men away from their families. When they return they find the Edwards homestead in flames. Aaron, his wife Martha (Dorothy Jordan), and their son Ben (Robert Lyden) are dead, and Debbie and her older sister Lucy (Pippa Scott) have been abducted.
After a brief funeral the men set out in pursuit. They come upon a burial ground of Comanches who were killed during the raid. Ethan mutilates one of the bodies. When they find the Comanche camp, Ethan recommends a frontal attack, but Clayton insists on a stealth approach to avoid killing the hostages. The camp is deserted, and further along the trail the men ride into an ambush. Though they fend off the attack, the Rangers are left with too few men to fight the Indians effectively. They return home, leaving Ethan to continue his search for the girls with only Lucy's fiancé, Brad Jorgensen (Harry Carey, Jr.) and Debbie's adopted brother, Martin Pawley (Jeffrey Hunter). Ethan finds Lucy brutally murdered and presumably raped in a canyon near the Comanche camp. In a blind rage, Brad rides directly into the Indian camp and is killed.
When winter arrives Ethan and Martin lose the trail and return to the Jorgensen ranch. Martin is enthusiastically welcomed by the Jorgensens' daughter Laurie (Vera Miles), and Ethan finds a letter waiting for him from a trader named Futterman (Peter Mamakos), who claims to have information about Debbie. Ethan, who would rather travel alone, leaves without Martin the next morning, but Laurie provides Martin with a horse to catch up. At Futterman's trading post, Ethan and Martin learn that Debbie has been taken by Scar (Henry Brandon), the chief of the Nawyecka band of Comanches. A year or more later, Laurie receives a letter from Martin describing the ongoing search. In reading the letter aloud, Laurie narrates the next few scenes, in which Ethan kills Futterman for trying to steal his money, Martin accidentally buys a Comanche wife (Beulah Archuletta), and the two men find a portion of Scar's band killed by soldiers.
The search leads Ethan and Martin to a military fort, and then to New Mexico, where a Mexican man leads them to Scar. They find Debbie after five years, now an adolescent (Natalie Wood), living as one of Scar's wives. She tells the men that she has become a Comanche, and wishes to remain with them. Ethan would rather see her dead than living as an Indian, and tries to shoot her, but Martin shields her with his body and a Comanche wounds Ethan with an arrow as they escape. Though Martin tends to Ethan's wound, he is furious with him for attempting to kill Debbie, and wishes him dead. "That'll be the day," Ethan replies, as they return home.
Meanwhile, Charlie McCorry (Ken Curtis) has been courting Laurie in Martin's absence. Ethan and Martin arrive home just as Charlie and Laurie's wedding is about to begin. After a fistfight between Martin and Charlie, a nervous "Yankee" soldier, Lt. Greenhill (Patrick Wayne), arrives with news that Ethan's half-crazy friend Mose Harper (Hank Worden) has located Scar. Clayton leads his men to the Comanche camp, this time for a direct attack, but Martin is allowed to sneak in ahead of the assault to find Debbie, who welcomes him. Martin kills Scar during the battle, and Ethan scalps him. Ethan then locates Debbie, and pursues her on horseback. Martin fears that he will shoot her as he has promised; but instead he sweeps her up onto his saddle. "Let’s go home," he says. Debbie is reunited with her family, and Martin with Laurie. In an iconic closing scene, Ethan departs the homestead as he arrived—alone—clutching his arm, the cabin door slowly shutting on his receding image.

Question: Why do Martin and Charlie get into a fight?
Answer: Charlie is about to marry Martin's girlfriend.
Alternative answer: Because Martin was courting Laurie