The film's plot involves three submarine mates, Ted Barker (James Stewart), Gunny Saks (Sid Silvers), and Mush Tracy (Buddy Ebsen), arriving in New York City after four years at sea. The film opens as their sub reaches New York harbor with the sailors singing "Rolling Home." Featured in the number are Gunny, Mush, Ted and a quartet called The Foursome.
As many of the sailors receive liberty, Gunny and Mush were denied shore leave until their Captain sends them to deliver a letter to Rear Admiral Stubbins. Nora Paige (Eleanor Powell), a singer and dancer, who has just lost out on a Broadway show, enters the Lonely Hearts Club suitcase in hand. The club's receptionist, Jenny (Una Merkel), offers to share her apartment with Nora. When she introduces Nora to the others at the club, Nora demonstrates her talents by singing and dancing to "Rap Tap on Wood" (Miss Powell's vocals are dubbed by Marjorie Lane). Also featured was The Foursome, a quartet of harmony singers, who also play a penny whistle and different sizes of ocarinas (also known as sweet potatoes).
Ginny tells Nora about her marriage to a sailor who was her partner in a twenty-eight day marathon dance. They conceived a daughter, Sally, in the two days they had together before he shipped out and she never told the guy he was a father. That guy was Gunny, who is anxious to rekindle a relationship with his wife. Meanwhile, Mush falls for a talented singer/waitress, Peppy Turner (Frances Langford).
Romance enters Nora's life in the form of Ted Barker. At their first meeting at the Lonely Hearts Club, Ted sings "Hey, Babe, Hey" to Nora as they dance. Then several other members of the cast sing a chorus including Nora, Gunny, Ginny, Peppy, Mush and the Foursome. The number ends with the sailors and their girl friends tap dancing. Later, Captain Percival Dingby (Raymond Walburn) announces Lucy James (Virginia Bruce), a famous actress, is coming aboard the sub. The men sing about her arrival. Once she comes aboard with her cute little dog under her arm, Miss James sings "Love Me, Love My Pekinese." During a photo session with the Captain, he drops her dog overboard; all the sailors dive in to rescue the pup. The next days newspaper features a photo of Ted handing the soaked dog to Miss James. McKay, her agent, immediately plots to cook up a romance between Ted and Lucy to generate publicity for her new show.
The next scene is one of the most, if not the most, famous musical sequence from the film. Ted begins crooning "Easy to Love" to Nora as they stroll in Central Park. After they kiss, Nora sings; they kiss again and she dances while Ted conducts an imaginary orchestra. A Central Park policeman (Reginald Gardiner) takes over the symphony maestro role as he directs the imaginary orchestra in a combination of Ponchielli's "Dance of the Hours" and "Easy to Love." By the end of the number, the policeman/conductor keels over in a dead faint.
Lucy and McKay arranged with Captain Dingby for Ted to have dinner with Lucy at the Club Continental. The evening's entertainment was Georges and Jalanas (Georges and Jalana appeared as themselves) ballroom dancing to "I've Got You Under My Skin." Ted had told Nora he would meet her later in Central Park, but, after waiting far past the appointed time, Nora dejectedly leaves.
The next morning's newspaper features a photo of Ted and Lucy together, which, of course, disturbs Nora. When Ted calls to apologize, she hangs up on him. Ted goes to McKay's office to bargain with him to give Nora a job in Lucy's new production, but he doesnt want Nora to know about their arrangement. McKay makes her Lucy's understudy.
Ginny, Sally, and Nora visit the sub, but Ginny still isn't sure she wants Gunny to know he has a daughter, so Nora claims Sally as her child. Ted assumes Nora is married and backs off.
Lucy begins to care for Ted and refuses to allow any further publicity about their relationship. She says if any more articles or photos appear in the newspapers she won't perform on opening night. During Ted's visit to Lucy's apartment, she confesses her increasing affection towards him by singing the film's most famous song, "I've Got You Under My Skin."
Peppy Turner reprises "Easy to Love" in a rehearsal of Lucy's show while the limber-limbed Mush, now out of the Navy, dances around her.
Lucy gets more and more upset. She doesnt like a costume and thinks the song's arrangement is undanceable. McKay asks Nora to dance to the arrangement, which she does brilliantly. When Lucy realizes what is happening, she demands McKay fire Nora, which, reluctantly, he does.
Ginny confesses to Ted, who is also out of the Navy now, that Sally is her child, not Nora's and that Nora loves him. She also tells him about Nora getting fired from the show. Ted calls the press and gives them a cooked up story. When the next morning headlines proclaim that Lucy James is going to marry an ex-sailor, she stays true to her threat and won't go on (which means, of course, that her understudy, Nora, would become the show's star).
The film's finale is a gigantic production number from the show, "Great Guns." Set on an Art Deco battleship, it opens with Peppy singing "Swingin' the Jinx Away," backed by a male chorus of singers and dancers. After some acrobatics by sailors, Mush takes his turn with the tune as he sings and dances backed by a female chorus of singers and dancers in front of the ship's stylized guns. After more singing by the male and female chorus, Peppy and the Foursome perform more of the song. Finally, Nora makes her entrance down the spiral stairs of the ship's superstructure and then slides to the stage via a pole. Dressed in a stylized drum major outfit, she taps to "Swingin' the Jinx Away" and then leads the band and chorus in "Hurrah for the Red, White and Blue," a very patriotic finale for a non-wartime movie.
Just before the credits roll, Ted congratulates Nora on a splendid performance and Ginny finally tells Gunny he's a father (unfortunately, he has already signed up for four more years in the Navy).