Williams was desperate to land the role as soon as she read the script. The movie is about the difficult relationship Monroe and Sir Laurence Olivier shared while making The Prince and the Showgirl.
Williams knew portraying the star would be a tall order though, so initially tried to make herself hate the role. When that didn't work and she won the part she set about preparing.
"I'd go to bed every night with a stack of books next to me," she said.
"And I'd fall asleep to movies of her. It was like when you were a kid and you'd put a book under your pillow hoping you'd get it by osmosis."
The 31-year-old star is looking forward to seeing how the movie is received. While at one point in her life she would have been nervous, that's not the case now.
She has a five-year-old daughter Matilda, her child with late actor Heath Ledger. Losing him and being a single mother has made her strong and she's now looking to the future.
"I feel like something has changed for me, but it's a new change, so it's going to be hard for me to describe. Maybe it has something to do with turning 30. I don't feel as shy or nervous or self-conscious. I have more confidence that I can handle what life brings me. I don't feel scared to have an idea and express it. I feel giddy about it because it's a complete transformation. It's like I've found my voice," she explained.
"I'm not lonely, and I think that has a lot to do with what's on my bedside table rather than what's in my bed."
Williams also admits the tragedy of losing Ledger has taught her to appreciate the more important things in life.
"Three years ago, it felt like we didn't have anything, and now my life - our life - has kind of repaired itself," she tells Vogue.
"(Ledger's death) changed how I see the world and how I interact on a daily basis. It's changed the parent I am ... It's changed the kind of work that I really want to do. It's become the lens through which I see life - that it's all impermanent."
Williams has also moved on in her personal life - she has found love with director Cary Fukunaga, two years after her split from another filmmaker, Spike Jonze.
- AAP