Although he wasn't aware of it at the time, Shizuo and Vorona first met during the battle at the Raira practice fields. Shizuo quickly gained Vorona's attention due to his inhuman strength and ferocity. Even though she technically failed her mission, she expressed nothing but excitement and joy at the prospect of fighting Shizuo again which becomes one of her primary motivations throughout the series.
Shizuo formally meets Vorona shortly after his boss hires her at Simon's recommendation. Shizuo's boss assigns Vorona to work under Shizuo, the official reason being that Shizuo is supposed to act as her mentor and show her the ropes (a task he accepts with much enthusiasm). The real reason, however, is so that Vorona can act as a deterrent towards Shizuo's tendency to cause untold amounts of collateral damage when angered. Basically, Vorona acts as the muscle when Tom begins to shakedown a client unless said client proves to be especially resilient. In which case, Shizuo is called in to take care of it.
Shizuo appears extremely excited with having a kouhai (underclassman/junior colleague) to work under him due to the fact that Shizuo normally gets fired before he can gain any sort of seniority wherever he works. Shizuo takes his role as mentor very seriously and treats Vorona like a protege through most of their initial interactions. As the series progresses, Shizuo begins to regard Vorona as not just his kouhai but also as a close friend in the same way as Tom or Celty.
Vorona appears to have a few more complications with regards to her relationship with Shizuo (most of which will be covered in the conflict section below). As stated earlier, Vorona's interest in Shizuo began with their fight at Raira. Since then, she has developed a strong, almost obsessive, desire to challenge him in combat once again. However, due to Vorona's naturally inquisitive nature, she also develops an interest in Shizuo as a person since he possesses many human and inhuman qualities. As such, she resolves to learn all that she can about Shizuo (personality traits, his past, as well as any weaknesses he might have) before finally killing him. As the two of them spend more time together and Vorona becomes more accustomed to life in Ikebukuro, this desire appears to grow less prominent in her mind as time goes on. She even discovers numerous likes and dislikes that she and Shizuo share, a primary example being their love of sweets. By the end of volume 10, it appears that Vorona seems to have developed a sense of gratitude toward Shizuo and Tom for welcoming her into their group. Izaya himself comments that the relationship between Shizuo and Vorona somewhat resembles the friendship between Kyouhei, Walker and Erika and as well assumed that Vorona has special feelings for Shizuo. Interestingly, others who have heard of Shizuo and are aware of his reputation (usually gangsters) as well as seeing Vorona with him have gotten that the wrong idea that Vorona is Shizuo's lover.
As stated earlier, the primary conflict between the two stems from Vorona's desire to kill Shizuo in combat (something Shizuo remains oblivious to). Although the desire has dimmed somewhat since she started working with him, this goal still remains strong in Vorona's mind as one of her primary motivations. As stated by Izaya in Volume 10, Vorona's obsession has grown to the point where Shizuo has become the only opponent she could have that could give her any form of excitement.