You can begin this quest by talking to Sibbi Black-Briar on the main floor of the Riften Jail.
He will give you a quest in which you need to discover the whereabouts of Svidi, a former lover of his.
Sibbi tells you he is in jail because he killed Svidi's brother after Svidi told him Sibbi had been cheating on her. Sibbi accidentally killed him in self defence and is the reason he is now in jail.
Svidi is the bard at the Vilemyr Inn in Ivarstead where she goes by the name of Lynly Star-Sung. After finding her she will give you her version of the story. She says that Sibbi and her were to be happily married and then says that Sibbi was also cheating on Svidi. Once she found out she asked her brother to confront Sibbi which ended in his death. After she tells you her story you will have two choices when you return to Sibbi. You can either tell him that she is hiding out in Ivarstead or lie to him.