Exposition: Once upon a time, there were two sisters. The younger daughter, named Bianca was a very sweet woman and had many suitors vying for her attention. The older was named Katherina, and she was very rude and known as a "shrew".
"Thinkest thou, Hortensio, though her father be very rich, any man is so very a fool to be married to hell?" Act I
Rising Action: Their father had a rule that he would not allow his younger daughter to get married until his older one, the shrew, had been married off. Bianca's suitors were doubtful that any sane man would ever wish to marry Kate, but they resigned themselves to finding one anyway.
"That is, not bestow my youngest daughter Before I have a husband for the elder" Act I
Rising action: Eventually a man is found by Hortensio, named Petruchio. Petruchio is looking for a wife from a rich family. Hortensio, being his friend, "helps" him out. Even though Kate is a shrew, Petruchio is determined to marry her and even though Kate doesn't entirely agree to it, Petruchio manages to convince her father to allow him to marry her
"Thou must be married to no man but me"-act II
Climax: After Petrucio and Kate arrive back at Petrucio's home, Petrucio begins to break down Kate's temperament. He starves her and wears down her wit. Eventually she breaks and becomes obedient, finding it more fun to joke with her husband than against him.
"An thus I'll curb her mad and headstrong humor."-act III
Falling Action:Meanwhile, Lucentio and Bianca are back at her father's house where Lucentio is acting as her tutor to get close to her. They get married in secret, because Bianca's father believes Lucentio's servant, Tranio, to be Lucentio and Lucentio to be a tutor.
I read that I profess, the Art to Love (Act III)
Resolution: At Bianca and Lucentio's wedding, a bet is made to see who's wife is the most obedient. Since Kate was last known as a shrew, all bets are against her, but in fact she is the most obedient. She comes and brings Bianca with her and berates her for not being more obedient to her husband.
"Why, there's a wench! Come on, and kiss me, Kate." (Act III scene IV)