After Sarah Paulson moved to New York City when she was a young girl, her mother took a job as a waitress at Sardi’s, a storied Broadway restaurant. It opened up a world that she would not have otherwise been exposed to, helping to nurture her ambitions of performing onstage.

Paulson’s first acting job, at 19, was as a Broadway understudy, beginning a career that returned to the stage several more times but found its rhythm on television, with steady roles on Ryan Murphy’s “American Horror Story” and a career-defining turn as the prosecutor Marcia Clark in the limited series “The People v. O.J. Simpson: American Crime Story,” for which she won an Emmy.

Despite complex roles as famous public figures and, once, a pair of conjoined twins, Paulson said her most challenging role has been in the Broadway drama “Appropriate,” for which she received a Tony nomination for best leading actress in a play on Tuesday.

In “Appropriate,” a play by Branden Jacobs-Jenkins, Paulson plays an older sister clinging to her memories of her father as she and her siblings clear out his home after his death, confronting the family’s dark secrets and their grievances against one another in the process. In the script, Paulson gets to play with cutting insults, weighty monologues and plenty of yelling.

After learning of the news while still in bed, hours before taking the stage again, Paulson spoke about the endurance that it takes to be a stage actor and about her career coming full circle. These are edited excerpts from the conversation.

Tell me how you’re feeling right now about your first Tony nomination.

I feel very moved and certainly overwhelmed to be in a category with such extraordinary women, some of whom are my friends. More than anything there’s that little girl in me who moved to New York at 5 years old and whose mother got a job as a waitress at this theater hangout, to wake up and have a Tony nomination for the first time in my life, at 49, feels just wildly moving to me and something that I have dreamed about since I was a girl.

I think a lot of times we spent a lot of energy pretending like these things don’t matter, because at the end of the day, they don’t — in the grand scheme of things the work is all that matters — but the little girl in me cannot be quieted this morning with a kind of explosive joy and excitement for a childhood dream being realized.

What makes your role in “Appropriate” — as Toni Lafayette, this very headstrong, sometimes caustic woman — the toughest you have faced so far?

Part of it is the athleticism required to do a play eight times a week — vocally, spiritually, emotionally. It is literally different every night. Energetically, you can only prepare a certain amount and then something else happens onstage between you and the audience and you can’t prepare yourself for that. There are aspects of every performance that are unknown to you.

I remember one of the notes I got — I actually have it pinned up on my wall in my dressing room now — is that Toni belongs to you now. Ride the roller coaster with her; when she’s her most cruel, do it. When she’s her most loving, do it. When she’s her most vulnerable, allow that to happen. Toni is a roller coaster. She’s a roller coaster of a person, and therefore I have to be on that rickety roller coaster with her every night.