Old Babtista was explaining to Hortensio, Petruchio, and Lucentio that Bianca wouldn't be married to any of them until Kate found a suitor. This was almost impossible because his daughter was Kate the cursed and she was a shrew. The suitors for Bianca repeatedly attempted to get to Bianca but they could not.
Petruchio wanted to be the suitor for Kate so he told old Babtista who was surprised. Kate was throwing a fit and destroying her bedroom, Petruchio kept his distance. He was trying to convince Kate that he could love her if she changed but she kept thrashing around and throwing objects at him.
Petruchio calms down Kate enough to announce that he and Kate will be getting married on Sunday. Old Babtista, Hortensio, and Lucentio looked surprised. Bianca could now find a suitor.
Lucentio acts quickly while pretending to be a tutor and wins Bianca's affection. Lucentio was also very wealthy and that won the fathers selection of a suitor.
To get control of Kate before the wedding, Petruchio acted like her by being angry at his servants. He didn't like both of the dinners that were cooked or the bedding. He starved Kate and deprived her of sleep; He then showed up to the wedding late while wearing horrible clothes. After all of this Kate learned to respect a husband.
Petruchio, Lucentio, and Hortensio bet on whose wives were the most obedient. Lucentio and Hortensio went before Petruchio and their wives made excuses to not come to the husbands. They doubted in Kate the cursed but she came to Petruchio while dragging The widow and Bianca and explaining how to respect your husbands.