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 that he is a lord.
In the play performed for Sly, the "Shrew" is Katherina Minola, the eldest daughter of Baptista Minola, a Lord in Padua. Katherina's temper is notorious, and extremely volatile, and it is thought that no man can control her, and no man would ever wish to marry her. On the other hand, her younger sister Bianca is nubile and much sought after by the nobles. Baptista however has sworn not to allow his younger daughter to marry before Katherina is wed, much to the despair of her suitors, Hortensio and Gremio, who agree that they will work together to marry off Katherina so that they will be free to compete for Bianca.
The plot becomes considerably more complex when two strangers, Petruchio and Lucentio, arrive in town (although not together). Lucentio, the son of the great Vincentio of Pisa, instantly falls in love with Bianca. Petruchio, for his part, seems interested only in money and fine jewels.
When Baptista mentions that the only men who will be permitted to attend Bianca are tutors, Hortensio disguises himself as a music tutor named Litio, and Lucentio disguises himself as Cambio, a tutor of philosophy. Gremio then encounters Lucentio, and presents him to Baptista, whilst Hortensio convinces Petruchio to present him to Baptista. Thus, Lucentio and Hortensio, pretending to be teachers, attempt to woo Bianca behind her father's back.
Meanwhile, Petruchio is told by Hortensio about the large dowry that would come with marrying Katherina. Petruchio quickly negotiates the dowry with Baptista, then marries Katherina in a farcical ceremony during which, amongst other things, he strikes the priest, and then takes her home against her will. Once there, he begins the "taming" of his new wife – he keeps her from sleeping by blowing a trumpet, invents reasons as to why she cannot eat, and buys her beautiful clothes only to rip them up with a crudely forged bread knife. When Katherina, profoundly shaken by her experiences, is told that they are to return to Padua for Bianca's wedding to Lucentio (actually Lucentio's servant Tranio in disguise), she is only too happy to comply. By the time they arrive however, Katherina's taming is complete and she is either unable or unwilling to resist Petruchio. She demonstrates her complete subordination to his will by agreeing that she will regard the moon as the sun, and the sun as the moon.
Meanwhile Bianca marries the real Lucentio, after the Lucentio/Tranio subterfuge is exposed, and Hortensio, realizing he has no hope of winning Bianca, marries a rich widow. During the banquet, Petruchio brags that his wife, formerly untameable, is now completely obedient. Baptista, Hortensio, and Lucentio are incredulous and the latter two believe that their wives are more obedient. Petruchio proposes a wager in which each will send a servant to call for their wives, and whichever wife comes most obediently will have won the wager for her husband. Katherina is the only one of the three who responds, winning for Petruchio the wager. At the end of the play, after the other two wives have been summoned, Katherina gives them a soundly-reasoned speech on the subject of why wives should always obey their husbands. The play ends with Baptista, Hortensio and Lucentio marvelling at how Petruchio has thoroughly tamed the shrew.