The 29-year-old was speaking at an enquiry into press intrusion at the Royal Courts of Justice in London.
She told how the media's intrusion had left her in a state of "complete anxiety and paranoia", and caused her to accuse those close to her of selling stories.
Previously, she said, she had felt "very protected".
"I am very lucky, I have a very tight group of friends and a very supportive family, and to this date no-one has ever sold a story on me," she said.
"But it was baffling how certain pieces of information kept coming out and the first initial steps I took were to change my mobile number.
"And then I changed it again and again, and I ended up changing it three times in three months."
She added: "Naturally, having changed my number and being pretty convinced that it couldn't be as a result of hacking, I accused my friends and family of selling stories and they accused each other as well."
The Alfie actress recalled one incident during which she gathered people in a room to question them when a story emerged about something only four people knew about.
She said she felt "terrible" when she realised no-one had spoken to the press.
The effect that it had on my life was really damaging to me and to my friends," commented the star, who said it was "unfathomable" that someone could feel comfortable hacking phones.
"Nobody could understand how this information was coming out," she said. "It was impossible to lead any kind of normal life at that time and that was very difficult for a young girl."
Sienna decided to take action against the paper after being presented with evidence by the police.
She settled out of court for £100,000 in damages and costs.
The media enquiry, which is being presided over by Lord Justice Leveson is looking at the "culture, practices and ethics of the media" and whether the self-regulation of the press works.
Well known figures giving evidence include Gerry and Kate McCann, Hugh Grant, JK Rowling and Max Mosley.