Prior to the first act, an induction frames the play as a "kind of history" played in front of a befuddled drunkard named Christopher Sly who is tricked into believing he is a lord.
In the play performed for Sly, the "shrew" is Katherina, the eldest daughter of Baptista Minola, a lord in Padua. Katherina's temper is notorious, and it is thought no man would ever wish to marry her. On the other hand, two men – Hortensio and Gremio – are eager to marry her younger sister Bianca. However, Baptista has sworn not to allow Bianca marry before Katherina is wed, much to the despair of her suitors, who agree to work together to marry off Katherina so they may freely compete for Bianca. The plot becomes more complex when Lucentio, who has recently come to Padua to attend university, falls in love with Bianca. Lucentio overhears Baptista announce he is on the lookout for tutors for his daughters, so he has his servant Tranio pretend to be him, while he disguises himself as a Latin tutor named Cambio, so he can woo Bianca behind Baptista's back.
In the meantime, Petruchio arrives in Padua from Verona, accompanied by his servant Grumio. He explains to Hortensio, an old friend of his, that he has set out to enjoy life after the death of his father, and his main goal is to wed. Hearing this, Hortensio recruits Petruchio as a suitor for Katherina. He also has Petruchio present to Baptista a music tutor named Litio (Hortensio himself in disguise). Thus, Lucentio and Hortensio, pretending to be the tutors Cambio and Litio, attempt to woo Bianca unbeknownst to her father, and to one another.
To counter Katherina's shrewish nature, Petruchio employs reverse psychology, pretending every harsh thing she says or does is kind and gentle. Katherina allows herself to become engaged to Petruchio, and they are married in a farcical ceremony during which he strikes the priest and drinks the communion wine. After the wedding, he takes her to his home against her will. Once they are gone, Gremio and Tranio (disguised as Lucentio) formally bid for Bianca, with Tranio easily outbidding Gremio. However, in his zeal to win, he promises much more than Lucentio actually possesses. When Baptista determines that once Lucentio's father confirms the dowry, Bianca and Tranio (i.e. Lucentio) can marry, Tranio decides they will need someone to pretend to be Vincentio, Lucentio's father. Meanwhile, Tranio persuades Hortensio that Bianca is not worthy of his attentions, thus removing Lucentio's remaining rival.
In Verona, Petruchio begins the "taming" of his new wife. She is refused food and clothing because nothing – according to Petruchio – is good enough for her; he claims perfectly cooked meat is overcooked, a beautiful dress doesn't fit right, and a stylish hat is not fashionable. He also disagrees with everything she says, forcing her to agree with everything he says, no matter how absurd; on their way back to Padua to attend Bianca's wedding, she agrees with Petruchio that the sun is the moon, and proclaims "if you please to call it a rush-candle,/Henceforth I vow it shall be so for me" (4.5.14–15). Along the way, they meet Vincentio, who is also on his way to Padua, and Katherina agrees with Petruchio when he declares that Vincentio is a woman, and then apologises to Vincentio when Petruchio tells her he is a man.
Back in Padua, Lucentio and Tranio convince a passing pedant to pretend to be Vincentio and confirm the dowry for Bianca. The man does so, and Baptista is happy for Bianca to wed Lucentio (still Tranio in disguise). Bianca, aware of the deception, then secretly elopes with the real Lucentio to get married. However, when Vincentio reaches Padua, he encounters the pedant, who claims to be Lucentio's father. Tranio (still disguised as Lucentio) appears, and the pedant acknowledges him to be his son Lucentio. There is much confusion, and the real Vincentio is set to be arrested, when the real Lucentio appears with his newly betrothed Bianca, revealing all to a bewildered Baptista and Vincentio. Lucentio explains everything, and all is forgiven by the two fathers.
Meanwhile, Hortensio has married a rich widow, and so in the final scene of the play there are three newly married couples; Bianca and Lucentio, the widow and Hortensio, and Katherina and Petruchio. Because of the general opinion that Petruchio is married to a shrew, a good-natured quarrel breaks out amongst the three men about whose wife is the most obedient. Petruchio proposes a wager whereby each will send a servant to call for their wives, and whichever comes most obediently will have won the wager for her husband. Katherina is the only one of the three who comes, winning the wager for Petruchio. She then hauls the other two wives into the room, giving a speech on why wives should always obey their husbands. The play ends with Baptista, Hortensio and Lucentio marvelling at how successfully Petruchio has tamed the shrew.