Beginning with Elizabeth's first private conversation with Jane after the Meryton ball it is evident that Elizabeth takes great pride in her discernment. She believes that her abilities to see and analyze people's characters for what they are are far above her sister's abilities. Elizabeth argues that Jane tends to like people too quickly and to "never see a fault in any body" (Ch. 4, Vol. 1). Elizabeth even further argues that Jane takes "the good of every body's character and make[s] it still better." In this scene, Elizabeth then thinks to herself that she has more "quickness of observation and less pliancy of temper than her sister." Hence, Elizabeth quickly discerns that Darcy and even Bingley's sisters are arrogant and conceited.
Also, because Wickham is far more friendly and outspoken than Darcy, Elizabeth quickly discerns that Wickham is by far the better person. Her ability to discern leads her to prejudicedly conclude that Darcy has a foul temper and treats everyone hatefully.
Darcy's letter to her makes Elizabeth realize that she has been blind, that she has never actually seen Darcy behave immorally, and that all the opinions she has formed about him are based on prejudice.
We begin to see Elizabeth act without pride in her discernment and without prejudice when she visits Pemberley with her aunt and uncle Gardiner. Elizabeth learns more things from Darcy's housekeeper that make her further realize just how foolishly she has judged Darcy. When she meets Darcy unexpectedly at Pemberley, she converses with him, introduces him to her aunt and uncle when asked, and even allows him to introduce her to his beloved sister.
Elizabeth's humility is fully developed once she learns what Darcy did to ensure that Wickham would marry Lydia. Elizabeth knows that the whole Bennet family owes their entire reputation to Darcy's goodness and is deeply grateful.