What Alice does in New Moon, really...
Alice arranges a party for Bella's 18th birthday. When the Cullens leave, Edward requests that Alice not say goodbye to Bella.
During her absence, Alice takes time to research her human family with what little clues she had from James and discovers that she had a sister named Cynthia and a niece. She also found her grave and discovered that the date on her tombstone matched that of her admission to the asylum.
Alice later rushes back to Forks when she has a vision of Bella jumping off a cliff, though Alice she did not see Jacob rescue Bella. Alice is confused to find Bella alive. After some explanation about the cliff jumping, she is more relaxed and goes hunting so she can stay for a while. She tells Bella what the Cullens have been up to and finds out how hard it was for Bella when they all left her.
Alice has a vision of Edward trying to die because Bella's "dead" and helps Bella get to Volterra, Italy to stop Edward from exposing himself to the world and being killed by the Volturi.
While there, Alice steals a yellow Porsche 911 Turbo to make it in time and Edward promises to buy her one as a thank you. She also asks Jasper not to come so she doesn't lose him that way. In the Volturi's headquarters, Alice convinces Aro that Bella will become a vampire in the future, allowing them to leave safely. By the time they return to Forks, their family is present to welcome them back and officially move back to town. Alice is the first of the Cullens who vote in favour of Bella being turned into a vampire, though she is reluctant to do it herself, as she had told Aro she would to save them at the time.