The introduction of the play wastes no time to demonstrate who the shrew is. Kate enters the play in all her glory, shouting and breaking things and frightening others right from the gate.
Petruchio is not exactly subtle in his intentions to tame said shrew either. He needs a wife with a good dowry, which Kate is known for, however no one is brave enough to marry her. Petruchio decides she's a good match and immediately sets about "taming" her.
Petruchio often speaks to the audience in the play in a convention known in theater as "breaking the fourth wall". The character Ferris Bueller uses it famously in the movie Ferris Bueller's Day Off.