Mr. Darcy starts out on the wrong foot, to his grave misfortune, disdaining Elizabeth Bennet as not good enough to tempt him to dance, a comment she unfortunately overhears. Darcy will rue the day he made that statement.
Naturally, having insulted Elizabeth (and made her hate him), he falls head over heels in love with her. His great motivation in life becomes to marry her. But this is a problem for him: not only does she have no money, which really doesn't matter, her family (except for her sister Jane) is more than a little strange. He does love Elizabeth, but her family—her father! her mother!—does he want to be allied with such a group of nonsensical folk when he is the great Lord Darcy?
But love reigns supreme. Therefore, Darcy overcomes his qualms and proposes to Elizabeth. It never once crosses his mind that she might say no to him, but he manages to propose in way so completely arrogant that, if she didn't already hate him for separating Bingley and Jane, it would have been enough to make her angry. As it is, he throws her into a fit of intense rage with his clueless proposal, telling her that he will deign to marry her despite her embarrassing family and lack of money. Elizabeth essentially tells him she wouldn't marry him if he were the last man on earth. In her fury, she gets across to him that she finds him extremely arrogant. He backs off, but his desire to marry her does not abate. He writes Elizabeth a letter explaining his behavior with regard to Wickham and apologizes for interfering in Jane and Bingley's relationship.
Darcy sees his chance again when Elizabeth and her aunt and uncle arrive to tour his grand estate of Pemberley, and he runs into her. Darcy's polite behavior during this visit—along with what Elizabeth gleans about him from his housekeeper and sister— certainly begins to soften her feelings toward him.
Darcy gets his chance to go from zero to hero when entices Wickham, who has run off with Lydia, to marry the wild Lydia, thus saving the Bennet family reputation. Darcy is motivated to open the check book, spend time in London, and do whatever it takes to get Wickham and Lydia to the altar if it will help him win over Elizabeth. Darcy perseveres and ultimately wins his true love. He learns to be less arrogant and Elizabeth learns that maybe she was too prejudiced against him.