Her efforts earned her an Independent Spirit Award for Best Actress in Santa Monica, Calif., Saturday, as well as a nomination going into Sunday's Oscar race. She picked up a Golden Globe Award for her performance, last month, as well.
Directed by Simon Curtis, the film is based on the memoir of Colin Clark, an assistant director on the 1957 film "The Prince and the Showgirl" who showed Monroe around England when she was there shooting the movie with Laurence Olivier, a classically trained actor and director alternately amazed and frustrated by Monroe's talent, substance abuse, insecurity and Americanized approach to acting.
Williams plays the troubled sex symbol in the film version of Clark's book, while British actor Eddie Redmayne plays Clark and Northern Irish Oscar nominee Kenneth Branagh plays Olivier.
"I'm not a singer or a dancer," Williams told reporters in New York recently. "I hadn't been on stage since I was 10 years old. And, in some ways because of that, I felt like a tremendous outpouring of joy. I felt like a little girl whose dreams came true for the first time. And I was able to tap into what I imagine made Marilyn Monroe so luminous in those singing and dancing numbers."
Williams is the mother of a 6-year-old daughter with late actor Heath Ledger and a former cast member of TV's "Dawson's Creek," who has earned accolades in the past for her work in the films "Blue Valentine" and "Brokeback Mountain."
The actress said she tried not to let herself be overwhelmed by the task of capturing the unique spirit of such a well-known figure in "My Week with Marilyn."
"What I experienced was when you're in that state, your critical mind has to turn off," explained Williams. "There's no room for it because you are remembering steps and lyrics. It's like patting your head and rubbing your tummy at the same time and maybe what makes the performances of hers so magical is that she's not thinking."
To successfully play Monroe, Williams said she needed "a tremendous amount of preparation and the willingness to start at the very beginning, to not know what to do to make mistakes along the do, to not be hard on myself for those and to realize that they are part of the process."
Asked what he learned about Monroe while making the movie, director Curtis, who was sitting beside Williams, replied: "One of the things we, Michelle and I, talked about regarding Marilyn was just how intelligent she was and we were both touched by Marilyn's hunger to be taken seriously as an actress.
"We both came to really admire and sympathize with her through our work on the film. And we hope audiences will do the same," he added.
So, is Williams a follower of the absorbing, Method-style of acting Monroe is seen embracing in "My Week with Marilyn?
"I suppose whatever works," Williams said. "For me, for this, I had never done anything that required so much technical know-how. This was the first attempt that I had made, really the first time I had actually admittedly started from the outside in. Because I knew I was going to have a very, very long way to go. Where I, Michelle, have wound up after 31 years physically is very different from Marilyn. And so for the first time, I started externally, which was a switch-up for me, but similar to Marilyn, I suppose. I'm not trained. I just popped in to classes now and then, read lots of books, and at 31, have made some kind of amalgamations, some sort of hodgepodge of my own personal experience, what I know works for me in the moment, what I have learned from other actors, what I've picked up from books, and I certainly don't know what I would call it."
She also pointed out when Monroe was acting, the inventors of the Method, in which actors attempt to actually conjure the feelings their characters are experiencing to convey realism, were some of the most highly regarded teachers in the United States.
"The people who were driving the Method were actually alive and in the room and how exciting would that have been?" Williams wondered. "To be directed by [Elia] Kazan and have [teacher Lee] Strasberg by your side. So, now we sort of get secondhand information. It's sort of the soup of the soup. It's passed on and similarly, literally, whatever works. I'm not beyond doing rain dances or whatever. I'm still experimenting, too. I'm still finding out what works for me. And I think the reason that keeps me acting, that keeps me excited about it, is that I'm still learning about it. The answers change and new information comes in all the time that transforms how I'm going to do what I'm going to do."
The actress admitted that, growing up, she was more interested in the image and mystique of Monroe than she was in her body of work. However, she has since become a fan of her oeuvre.
Among her favorites, she revealed, is the classic "Some Like It Hot.
"I'm also pretty fond of 'The Misfits,' maybe because it was a shot, sort of her only shot, she had problems with the role, but it was her only shot at a serious part," Williams noted.
She went on to say she wishes Monroe could have experienced the freedom she has to choose her own projects. Monroe died in 1962 of a drug overdose at age 36.
"To work outside the studio system, to not be bound to playing the same roles, to not be a contract player," Williams reasoned. "To not, basically, be on salary and not have to take what's given to you. I wish she had a good experience with choices and independence."
"My Week with Marilyn" is in theaters now.
Celebrity Families of 2014 [PHOTOS]