Italy's is a melting pot with a lot of different cultural differences from region to region. How were the people united with such stark differences? Clearly today, there's still a Northern/Southern difference.
I have a comment where I touch on the Southern Question a bit here. You may find some of that discussion interesting, though it is more social and economic history than cultural.
I also have a post here where I talk about the difficulties of political union here.
Of course, there is more to be said on your question about cultural unification. I'm not an expert in Giuseppe Verdi or Risorgimental opera, but some recent scholarship -- most notably Alberto Banti's The Nation of the Risorgimento: Kinship, Sanctity, and Honour in the Origins of Unified Italy -- argues that Italian identity was less a cohesive series of ideas and more commonly manifested in common tropes and artifacts in many art forms which expressed nationalist ideas in opera, poetry and art. Banti calls these 'deep images' common cultural reference points that point to national identity in novel way. In popular poet Giovani Berchet's Matilde, the titular character has a nightmare that her father wishes to marry her off to an Austrian soldier, prompting her to plead with him to not mix the blood of the oppressed with the oppressor. In Verdi's opera Nabucco, the biblical king Nebuchadnezzar stands in as an allegory for Austrian brutality against the promised people (which are, again, allegorically the Jews but coded as Italian). There are such common artifacts of reference in many of these cultural works that give pre-unitary Italian nationalism a sense of both religious and moral importance which render themselves quite evidently in the language of nationalism itself. In poetry Italy may be represented by an oppressed maiden, but in the transcendent fantasy of nationalists the importance of la patria was just short of the divine.
Of course, these ideas become much more complicated after Italy's difficult unification where the fitful tensions between liberals, Catholics and moderates rendered an Italian state which left Catholics largely outside of its operation in the latter half of the nineteenth century. As such, these shared cultural references for nationalists became less common as liberals eschewed the divine language of sainthood and family for the more mundane language of politics. As I go into in the other posts, Italy as an abstract idea before unification was much more cohesive than the Italy that united in 1861, and the Italian state struggled mightily to govern a nation that was, while united in a geographical sense, severely divided socially and politically.