Wickham's father worked for Darcy's father. Wickham's father was a good man (unlike his son), and Darcy's father became godfather to Wickham. Although Wickham claims that Darcy's father promised him a living, this is not so. Darcy watched Wickham become a drunk, and a womanizer, and refused to provide the allegedly promised "living" to Wickham. Wickham then attempted to seduce Darcy's younger sister, Georgianna, and later lied to Elizabeth about the past dealings between himself and Darcy. Elizabeth believes him, and does not find out the truth until later in the book.
When Mr. Wickham and Mr. Darcy were kids.