The entire book is centered around the changing relationship between these two main characters; how they feel about each other, and the relationship that they have with one another is incredibly dynamic. It is constantly changing and shifting.
In the beginning, their relationship is one of strangers who form hasty judgments of one anothers. Darcy, as he admits at the ball to a friend, thinks Elizabeth isn't necessarily very attractive or special at all, although later he admits that she has "fine eyes" and is less of a social disaster than her younger sisters. Because Elizabeth heard Darcy's first comment, and because of his rather aloof attitude at the ball, concludes that Darcy is a snob, and dimisses him from her thoughts as unworthy of note. So to start off, they almost have an antagonist relationship.
Darcy's attitude towards Elizabeth changes for the better almost immediately, and continues to grow through the novel. He admires her spunk, individuality and sureness of mind. He grows to love her. For quite some time, however, that love is unrequited. Elizabeth continues to dislike him; this dislike is further fueled by the erroneous claims of the charming Wickham. She is downright rude and accusatory to Darcy, furthering their contentious relationship.
After Darcy explains himself in his letter to her after his first rejected proposal, Elizabeth feel horrible. Her attitude towards Darcy starts to change. She realizes that he is a true and loyal friend who acts on principle, adn that she was wrong about Wickham. When she visits his home and hears high praise sung by his servants, and sees his friendliness towards her aunt and uncle, she learns to love him even more. Then, when he helps out with the Lydia situation, her love is fixed.
So, their relationship goes from contentious and unsteady, to one of solid affection and respect. I hope that helped; good luck!