Norah Jones: It's always the quiet ones

We head downtown to lunch, and she is noticeably at ease once we've left the sterile hotel lounge and the glare of the photoshoot she has just completed. "It was cool," she says, placid and even-handed, a tone she maintains throughout. Voluble, she's not. As we walk, her eyes fix on the giant, shiny new buildings around her; she marvels at the construction transforming the gritty urban landscape. She's lived in the neighbourhood for many years, but is considering a move out of Manhattan, across the East River to Brooklyn. There's a sense that she, too, is evolving after her breakthrough success eight years ago.

Several times during our time together she says "now that I'm older" - although she's only 30. The statement is laden with the consequences of having achieved spectacular success at 22, an age when most people are just beginning to work out who they are and what they want. Jones was too busy working, thrust into a whirlwind journey with high-stakes recognition - and feeling, at times, like an imposter.

How did she handle the inevitable aftermath? She's grown up a lot. Being off the road, making choices on her own, in charge of her own time. It has been another kind of journey: an interior one. She has been searching for how to feel valued beyond the public adoration. There are hints of a mini existential crisis: working out where she fits in and how she matters.

There have also been endings - or, as she puts it, "transitions". Break-ups with her band and her longtime boyfriend prompted her to take stock and led her, of all places, to church, which she attends regularly. It was not divine intervention she was looking for but perspective.

What's most distinctive about Jones is that she seems so normal. Normal enough to slip by paparazzi unnoticed, or to walk down the street without sunglasses or security. Normal enough to remain modest, considering her father is Ravi Shankar, "the greatest Indian musician on the planet", who has performed with Yehudi Menuhin and the Beatles.

Considering that at the age of 20 she dropped out of university in Texas with no real agenda other than to move to New York and become a jazz singer - and in little more than two years, in 2003, saw her debut album, Come Away with Me, win her eight Grammy awards; and considering her next release is likely to push her total album sales above 40m, one wonders why it didn't swell her head, why it didn't degenerate into the sex, drugs and notoriety of the Amy Winehouse sisterhood. She became a household name, turning a respected fringe genre of music mainstream; you couldn't go into Starbucks or sit in a dentist's chair without hearing her sultry vocals. It was the kind of success X Factor winners would kill for - stardom without being mortgaged to management companies.

And yet the success made her uncomfortable. When asked what it was that surprised her most about it she says: "That it happened at all." She had always been musically confident, but the rest of it threw her. "I felt like I was in an alien world." The furniture of fame, the interviews, the smiling for the cameras, the marketing of the brand, the machinery of what to wear and how to respond. "I just wasn't savvy with how to handle it."

Shrewdness is not a quality one associates with Jones, but it's clear she's learnt not just where her limits are but how to enforce them: "I know what I have to do to get the record out there and what I can't do, what I won't do." When she says this her tone and manner are soft, but there is a steely determination and firmness.

What made Jones so popular? She was the antithesis of the manufactured pop star - perhaps that was the point - a serious musician with serious talent. Her popularity paved the way for the re-emergence of jazz-focused female vocalists such as Amy Winehouse, though the singers couldn't be more different. "I've heard her, of course. I bought her record and I thought it was great." She pauses. "It's sad her life has overshadowed the music. She has a great voice."

And therein lies the clue to Jones's success and her ability to cope with it. Nothing is allowed to overshadow the music: no antisocial behaviour, no plunge into the gutter, no search for anonymous approval. You won't see her in the tabloids spilling out of a nightclub or rushed into rehab. What's frequently attributed to her is "maturity beyond her years" and, with this, the notion that she is boring - "Snore-ah Jones".

"I like to have fun and be silly and be a dork," she says in meek protest. "But sure, sometimes it's hard," she adds, revealing such verdicts can hurt. But probing deeper into Jones's personality proves frustrating. Is it a brick wall she's thrown up or have the critics diagnosed correctly? When asked if she gets depressed, she offers a chirpy "Not really. I'm a pretty cheery person."

She doesn't go to the music-video awards, has never been to a fashion show, and avoids the red carpet - except once, in 2007, when she attended the Cannes film festival. It terrified her. When she went to the Grammys the year she swept them, she used the back door because she was nervous. But why? "When I get a pedicure I'll read People magazine. I see all the Dos and Don'ts. I don't want to be a Don't."

So she isn't as comfortable as she appears. The subject of her family has been designated off-limits - she doesn't like talking about them. Is that another clue? Jones was born in 1979 in Brooklyn, New York, but her parents never married and when she was four her American mother, Sue Jones, moved them to Grapevine, Texas, a suburb of Dallas. The only child of a single mum, she knew who her dad was, but saw him infrequently until she was nine. After that, she didn't see him again or speak to him until she was 18.

Being the only child of a single mother is a defining existence. "You don't really know until you're an adult that you were in a bubble. But it was also fun. My mom and I took a lot of road trips and she is a kind of eccentric woman, not afraid at all - and as a result I was always a little fearful, probably because she was always forging ahead."

She is still very close to her mother and considers her a confidante. "We have a very intense relationship. I have other family on her side - and I have my dad and my half-sister and my stepmother, who I've gotten very close to, but we didn't grow up together, so it's not the same."

Growing up, stardom was never on her radar, not with the type of music she made. But would she have been content making music in obscurity? "I'm sure I would have frustrations, but I wouldn't have wished I was Beyoncé. My goals are to live comfortably and play music."

I sense there's more - she's not just private, she's guarded and vulnerable. But to what? Jones's musical identity was formed early on. Her mother, who is from Oklahoma, worked in the film business and put her in the church choir at the age of five. As a nine-year-old she listened to a lot of Billie Holiday - and even if she didn't understand the lyrics, she was hooked. Though she was gifted at music, she wasn't disciplined. The turning point came when she was 13 and found a piano teacher in Dallas who encouraged her. After that, she went to a high school for the arts that specialised in jazz.

Did she know she had talent? She shrugs. "I knew that when I sang, people were surprised." Jones attended the University of North Texas and took mainly jazz classes. Two years in, she realised that she hadn't met the academic requirements to get a degree. Her sole ambition was to play music, so she left at the age of 20 for New York and never returned. Friends she had made back in Texas helped her infiltrate the Manhattan jazz scene. Jesse Harris, the musician and songwriter (who wrote her hit Don't Know Why) became a close friend. But after six months she got disheartened playing gigs in restaurants and waitressing and was ready to return to Texas. "I'd gained weight - waiting tables, I was eating a lot of corn muffins and I didn't know they were filled with butter. I felt fat, I felt gross. I called my mom crying and said I wanted to go back to Texas. But my mom said, you know, you've only been there six months; at least give it a full year. I thought that was cool considering she didn't really want me there."

Things started to turn around - fast. She met Lee Alexander, who became her bass player and boyfriend, and they formed a band with Harris and others. She started playing more gigs and recording, leading to an album with the legendary Blue Note Records. She thought it might sell a few thousand copies. It sold 10m in the US alone. "I was flabbergasted," she says.

Jones is aware that there's nowhere to go but down in terms of sales, but this doesn't consume her with dread. "Anything I do is not going to be as successful as the first album. I was lucky financially - hopefully I'll still be able to have my dream, which is to not wait tables."

Inevitably, her success was linked to her father, even though their musical trajectories were entirely separate. I return to the off-limits territory. Did she feel a void growing up without him? "I didn't know any different. As I got older I felt it. [Now] we're as close as we can be. He doesn't hear very well, so he's hard to talk to on the phone. But I see him a few times a year. We've both done the best that we could. I feel good about where we are. I feel really lucky that he's still around - he's a pretty young 89. He still plays. I don't think he tries to take credit. He's proud of me."

What's driving her now is having fun. Her new album, The Fall, is a big departure - it is the first album she's made without her old band. She doesn't rule out playing with them again, but she has split with her boyfriend, Lee. He is nine years older than her and was by her side during the tornado of public attention and scrutiny. "We've gone through a lot together. The hope is that we can play music again."

After the last tour, Jones took some time off. She fixed up her apartment, got a dog, did gigs in small clubs, went camping with girlfriends, hung out at home and joined a book club. She also made a movie, My Blueberry Nights, with Jude Law. She had no ambition to be an actress but "it seemed like fun". The Hong Kong film-maker Wong Kar-Wai approached her out of the blue. The role, a young woman on a soul-searching trip across America, must have resonated. She retains a tight group of friends and jokes that her emotional security depends on how many drinks she's had, evading my invitation to a deeper conversation. For all the heart and soul of her songs, in person she has barriers she will not dismantle - they are reinforced when she feels confronted. Do you go to therapy? She gasps - answering the question without saying anything. "That's a personal question! Well, I think I get emotional when emotional things are happening to me. I'm pretty good at having a mask on. Having a stone face and not letting it show. But maybe not… I'm pretty transparent."

Are you a neurotic person? "I have my fair share."About what? "I have my moments." Insecure? "Only about what I'm going to wear. I'm not very fashionable. But I'm getting better." She admits she doesn't know if she would have had the stamina to stick it out in New York if she'd had to. She's made the most of the opportunities, worked hard, and is aware too that others might resent the fact she didn't claw her way up. She is not lazy, nor is she indifferent to her success, but she is not a self-promoter because she has never had to be. "I agree. I've been very lucky and things have come to me easy. But we all have our own private struggles."

When asked what she struggles with, there is a pause. She looks down, and the defences slip. "Plenty of stuff. Relationships. My relationship with family and friends. It's stuff I can't talk about because it involves other people." And suddenly Norah opens up - just a little. "I've started going to church recently," she says. "You asked me about therapy - I've had a hard few years." She says she's not a religious person, more spiritual, but she goes every week. It's a liberal church, down the street from where she lives, with a homeless shelter and soup kitchen, where she volunteered. It was a sobering experience. "I feel like I'm doing something worthwhile."

Her bigger ambitions are to get married and have a family, but she's in no rush. She's in a new relationship but won't discuss it. "I've never been in this situation before. It's always been out in the open, so I'm proceeding with caution." When asked if he's a musician, she squirms. "It's hard for me to know how to do this. It feels kind of lame. I want to be protective." She talks about her dog instead. "He's a poodle," she says. "They get a bad rap but they're great dogs."

Perhaps her relationships with her old band and her ex-boyfriend are still raw. "Working with the person you're involved with takes its toll." She had been with Lee since she was 20. She's hinted at the impact the transitions have had: they've emboldened her on one hand but also forced her to confront being on her own.

"It's tough…" she says, looking as though she has momentarily disappeared somewhere deep inside herself. Then, she brightens. "It will make you go to church and get a dog."

Norah Jones's new single, Chasing Pirates, and album, The Fall, are out on November 16