Edward Lewis, a successful corporate raider in Los Angeles on business, accidentally ends up on Hollywood Boulevard, in the city's red-light district after being rejected and breaking up with his girlfriend during an unpleasant phone call in which Lewis appears highly controlling; he asked his girlfriend to escort him during his California business trip, but she was offended that he could demand from her whatever he wants, as if she is his 'beck and call girl'. After leaving the party where he had this unpleasant phone call, taking his lawyer's Lotus Esprit luxury car, Lewis encounters a prostitute named Vivian Ward. He stops for her, apparently lost and having difficulties driving the car, asking for directions back to Beverly Hills. It is not clear if he really wants to hire her, or just get help getting back to his hotel. He asks her to get in the car and show him how to return to the Beverly Hills Regent where he is staying. It becomes clear that Vivian knows more about the Lotus than he does, and he lets her drive him to his hotel. Vivian charges Lewis $20 for the ride, and then they separate. He goes to his hotel, and she goes to the bus stop to go back to Hollywood Blvd. Lewis goes back to find Vivian waiting for the bus, and decides to hire her for the night, and then later, to play the role his girlfriend had refused, offering Vivian $3000 to stay with him for the next six days as well as paying for a new, more acceptable wardrobe for Vivian. Edward is visibly moved by her transformation from hooker to sophisticated woman, and begins seeing Vivian in a different light. He begins to open up to her, revealing his personal and business lives.
Edward takes Vivian to a polo match he sponsors in hopes of networking for his business deal. His attorney Phillip begins to suspect Vivian to be a corporate spy. Edward reassures him by telling him how they truly met and Phillip approaches Vivian, suggesting they do business once her work with Edward is finished. Insulted by Phillip and furious that Edward has revealed the secret of who she really is, Vivian wants to end her arrangement with Edward. Edward confesses to feeling jealous of a business associate who has paid Vivian some personal attention during the week. Vivian's straightforward personality is rubbing off on Edward and he finds himself acting contrary to his normal personal and business personalities. Clearly growing closer, Edward flies with Vivian in his private jet to see La Traviata in San Francisco. Vivian is moved to tears by the story of the prostitute who falls in love with a rich man, further edifying Edward's feelings towards Vivian. After the opera Edward appears to have truly fallen in love with Vivian.
Growing extremely fond of Edward, Vivian breaks her "no kissing on the mouth" rule and finds she is falling in love with him. He offers to put her up in an apartment so she can be off the streets but she rejects it, insulted and says this is not the "fairy tale" she dreamed of where a knight on a white horse rescues her.
In meeting with business associates whose company he is in the process of "raiding", Edward changes his mind at the last minute. His time with Vivian has shown him a different way of looking at life and he suggests working together to help save the associate's company rather than tearing it apart and selling it off for a profit. They will build big ships together. That was Edward's dream: to build things, instead of tearing them down. Furious over the loss of so much money, Phillip goes to the hotel to confront Edward, but finds only Vivian. He blames her for changing Edward and attempts to force himself on her. She is fighting him off as Edward arrives just in time to stop Phillip, hitting him while chastising him for his greed. He fires Phillip and then throws him out.
With his business in L.A. complete and his return to N.Y. imminent, Edward tries to persuade Vivian to stay one more night with him because she wants to, not because he's paying her but she refuses. On his way to the airport, Edward re-thinks his life and his unexpected feelings for Vivian. He has the hotel chauffeur detour to Vivian's apartment building where he leaps from the white limo and "rescues her"; a visual urban metaphor for the knight on a white horse rescuing the princess, fulfilling Vivian's childhood fantasy.

Question: How do Edward and Viviian first meet?
Answer: She's working as a call girl and he asks her for directions back to his hotel in Beverly Hills.
Alternative answer: On the street, as Edward is lost and having trouble with his car.