Most good stories start with a fundamental list of ingredients: the initial situation, conflict, complication, climax, suspense, denouement, and conclusion. Great writers sometimes shake up the recipe and add some spice.
Initial Situation
Kate's shrewish behavior and attitude leave her with zero marriage prospects and a difficult relationship with her family. Petruchio is looking for a rich wife.
Poor Bianca can't have boyfriends or get married until her older sister Kate gets hitched. The problem is that nobody wants to marry Kate because she's a total shrew. Good thing Petruchio arrives in town looking for a rich wife. He decides to marry Kate (sight unseen) despite the fact that she has a reputation for castrating men with her words. Petruchio heads over to Baptista's place to make a deal.
Conflict
Baptista says Petruchio can marry Kate but Kate hates Petruchio and continues to be a shrew.
It doesn't take much to convince Baptista that Petruchio should be allowed to marry Kate. Baptista says Kate must give the green light but the deal is pretty much done before Petruchio even sees Katherine. When the two meet, Kate is insulting and the two verbally spar for a few rounds. She wants nothing to do with Petruchio but he announces that Kate has no choice in the matter – he wants her and that's that.
Complication
Petruchio marries Kate and begins his shrew-taming campaign.
Poor Kate – Petruchio shows up late for the wedding ceremony and then proceeds to act like wild and crazy when he arrives. Once married, Kate becomes his legal "property," so she has to do what Petruchio says. When Petruchio says she'll go to bed hungry, that's what she does. If he wants her to dress in rags, she has no choice. Kate, however, won't keep her quiet. She continues to quarrel with Petruchio. This causes Petruchio to tighten the screws and Kate is made even more miserable.
Climax
Kate submits to Petruchio's will on the road to Padua.
On the way to Bianca's wedding, Petruchio threatens to make them turn back home if Kate doesn't agree with everything he says. Finally, Kate breaks down and plays along when Petruchio insists the sun is the moon and the old man on the road is a beautiful maiden. This is the turning point in the relationship, as Katherine submits to Petruchio's will and continues to obey her husband's every whim from here on out.
Suspense
Everybody says Kate is still a shrew. Petruchio bets that she's the most obedient wife.
At Bianca's wedding banquet, the wedding guests tease Petruchio about his shrewish wife. So, Petruchio makes a wager – whoever has the most obedient wife wins a big pot of cash. Hortensio and Lucentio decide to take his bet – after all, they've seen Kate at her absolute worst and assume she hasn't changed.
Denouement
Petruchio wins the bet. Kate delivers a speech about a woman's obligation to obey her husband.
When Petruchio calls for Kate, she comes running and Petruchio wins the bet. (The other wives ignore their husbands when called.) To top it off, Kate gets on her knees and fondles Petruchio's feet after she delivers a lengthy speech that lets everyone know that she's changed her evil ways.
Conclusion
Petruchio and Kate run off to bed.
Outwardly, it appears that order has been restored. Kate has transformed from shrew to obedient wife and all their friends and family believe she's a new woman. Kate and Petruchio run off to bed together.