Just off Fifth Avenue in Manhattan is an apartment Marie Antoinette would have killed for. Formal, spacious, elegantly furnished with brocade sofas and French antiques under vaulted ceilings, it is a mini-Versailles duplex in a classic pre-war building. Suddenly a familiar voice, raspy and cheerful, comes from the room above: "Okeey dokeey."

It could be the sound a woman makes on completing a final check in the mirror before she presents herself to the world. In this case, it's a cue that it's time to receive visitors. Once ushered upstairs, I realise that the home, like its owner, is easily misunderstood. Only the two main rooms downstairs convey grandeur on a colossal scale; upstairs it's a tasteful and civilised sanctuary for a woman who's built a career out of being fearlessly unrefined.

Joan Rivers is holding a Christian Louboutin stiletto shoe in the palm of her hand like a priceless sculpture. She is looking glam: tiny black dress on her tiny body, white leather jacket, fishnet stockings, red silk pumps. Impressive considering the time of day (8.30am). Driven mainly by the love of what she does but also by the fear that it could vanish tomorrow, she covets a demanding schedule. At 7.45am she was in full swing, on the phone commenting on the latest celebrity gossip on a radio talk show. "Heather Mills? Oh, please! I'm so bored with her blaming the media. You married him! You could stand it the whole time you were dating. So go behind the gates of your million-dollar house and the media can't get to you. I'm not worried about her. She'll be set for life."

A make-up team has gathered in her dressing room. Tonight, Rivers has a performance in New Jersey and this will have to take her through her heavily booked day until she goes on stage in the evening. On a regular morning, she wakes up at 8am with her dogs, gets dressed, drinks decaf coffee, and has some Cheerios with Cool Whip (a brand of imitation whipped cream). "It's what white trash eat. My refrigerator screams 'poor white trash', " she laughs.

In person, her stage persona - the coruscating, raucous wit - is softened by a silly streak and a nurturing presence. She is flawlessly groomed. "I like to look nice when I go out, because whenever someone says they saw someone famous, the first thing anyone will ask is, 'How'd she look?' " she says. Rivers, who has just turned 73, was once asked by a reporter exactly how many plastic-surgery procedures she's had. She told him 119 - and he took note. The truth is, she's had two full face-lifts and lots of little touch-ups. "Age sucks. I've never looked in the mirror and been happy. But then I wouldn't be me. I'd be a pretty woman - without a job. You know how you have some friends who are very unattractive but they think they're hot? They're very lucky." And the solution? "Don't go out! If you're really ugly, stay home. It's better in the long run. Or wear a burqa. How great is that? You don't know what your thighs look like!"

We descend the narrow staircase, past bookshelves filled with biographies and histories, and there is a book of sizable girth titled Jews in Sports. "I thought it was a joke," she says, looking down, making sure she doesn't trip. As we wait for the elevator to arrive, a large Burberry bag in her foyer catches my eye. She explains that the day before there was a sale and she had a huge credit note. "A dear friend gave me a caviar server the size of China and I took one look and thought, 'Never - there is no one I know that's worth that much caviar.' And there's nothing I love more than to watch New York women murder each other over a sweater."

As if Rivers doesn't have enough going on - a relentless performing schedule, a chat show in the works, and the Joan Rivers Classics Collection of jewellery for the shopping channel QVC (launched in 1990, it's made over $425m in sales) - she also presides over the board that vets tenants in her building and keeps them in line. She talks to the elevator operator about a notice that needs to be posted. "We can't use the doorman's phone to make personal calls - it's for emergencies only. We can't smoke in the lobby. And can't we recharge our BlackBerrys in our own apartments?"

With Rivers, there's never a dull moment because there's never a silent moment. She is constantly cracking jokes, suggesting ideas, sorting plans. Downstairs we wait for the black SUV to arrive, to drive us to a recording for Channel 4. "Make a right, then right and another right and a U," she tells the driver, as we slug through the Upper East Side traffic. As she points, her sleeve is raised and it reveals a home-made bracelet that says "Grandma". Her daughter, Melissa, has a five-year-old son, Cooper, and Rivers loves being called Grandma. Being a grandma is, naturally, part of her act. "Everyone thinks their grandchildren are the smartest. I'd like to meet someone who says, 'My grandson is a moron.' Who are these hideous people working at 7-Eleven? They were all brilliant kids?"

There is a seamlessness between her act and reality that makes it hard to distinguish between Joan Rivers, comedienne, and Joan Rivers, mother and grandmother. Does being funny feel like work? "It's not work. I'm funny naturally, I know. But when it's your job, and you're going on a show, you can't rely on personality. So I prepare. I over-prepare. If I'm not getting a laugh, I go right into something else that will make it work." And on days when she doesn't feel funny? "I never have those days. I see everything as funny. It's ruined my life. Everything. I did jokes two days after 9/11, and Melissa lost friends. But that's how I cope."

The hotel suite is overheated and packed. Her only instruction is to the lighting engineer. "Please make sure all the other women on this show look hideous so that everyone says how great Joan Rivers looks." He laughs. Back in the car, en route to her office, where she will do another radio show before a QVC meeting to discuss the UK launch, she explains her reluctance to analyse humour. "You can't analyse it. Woody Allen once said to me if it's funny you fall on your knees and say, 'Thank you, God.' People agonise over 'Is banana a funnier word than apple?' You should know it - that's what makes it funny." But she is eager to explain why she thinks men don't find funny women sexy. "I think that men truly don't want to be topped. It's hard to be with someone brighter and faster and smarter than you. I can't remember laughing till I cried at something Pamela Anderson said. When was the last time someone said, 'Oh, Pam, stop, you're killing me!'"? Rivers has high standards when it comes to humour, and Prince Charles has made the cut. "Prince Charles, who I worship, has the best sense of humour. The best. Camilla too. I met them at a charity function - she and I both do osteoporosis - and we met at a large dinner for the Prince's Trust. I met the duchess and I said something about Cher, 'She likes men so young that she hangs out at Toys 'R' Us.' And she laughed." Rivers was one of only four Americans invited to the royal wedding, and says the best part was the atmosphere. "I've never seen a wedding ever - ever - where everybody was happy. When I go to weddings it's usually 'How much longer?' or 'That bitch, she got him finally.' "

It is still only 10.30am when we arrive at her office, which is feminine and modern, with her Emmy award on the shelf alongside photos of Melissa, her grandson, and Prince Charles and his dog. While she sits at her desk, waiting to go on air again, she tells me she doesn't like to eat after 3 or 4pm. And at night, when she's alone, it's her time to unwind. "I paint or I read or I do crossword puzzles."

Before we leave, Rivers indicates her favourite ornament: a wooden ship. "After my husband, Edgar, committed suicide [in 1987], it was a very hard time for us. Melissa brought this all the way back from the Bahamas for me." She points to its name: Unsinkable.

Joan Rivers was born in Brooklyn to Russian immigrant parents, Beatrice and Meyer Molinsky. She believes she inherited humour from her father, a doctor. On a fishing trip with him, she remembers making the grown-ups laugh was a distinctive thrill. She graduated hoping to become an actress but, with no money, took a job as a buyer for a department store and for seven years did comedy at strip clubs and coffee shops. Then, in 1964, there was a shift. She'd previously performed other people's material but she began speaking about what she thought was important. Having audiences laugh at what she thought was funny was galvanising and, in 1965, she was booked on The Tonight Show, the dream for every aspiring comic. Soon afterwards she married Edgar Rosenberg, a British producer. Their daughter, Melissa, was born in 1968. Rivers built a reputation on jokes about her failures and inadequacies. "Once you expose your insecurities, they can't get you," she says. "You can't say I'm fat and old: I've already said it. So you think you're hurting me? You're not. Humour is a great defence."

She admits people take the upper hand with her, but it doesn't seem to trouble her. "My friends walk all over me - I'm never considered; I'm never a leader. That's fine. I'm a leader where I want to be - on stage. That's my kingdom."

In the 1980s, her kingdom was booming. She lived in a mansion in Bel Air, and from 1983 to 1986 she was the permanent guest host on The Tonight Show when Johnny Carson was away. She was selling out concerts at Carnegie Hall, headlining in Vegas, her albums were hits and her books bestsellers. She did six one-hour BBC specials, Joan Rivers: Can We Talk? But then it seemed to collapse overnight. Knowing she would never be named as Carson's successor, she left to present her own show on the new Fox network. Carson never forgave her. His stamp of disapproval, and the cancellation of her Fox show after just seven months, started the downward spiral. Then, in 1987, her husband committed suicide in a Philadelphia hotel room. He'd been depressed and clashed with network executives over the ratings of her show. "I had no choice but to come out of it, because of Melissa," she says. "What's the choice? To kill myself and leave that legacy - Mommy and Daddy? You gotta say, 'Look, I'll get through it.' And women are strong. Especially Jewish women."

For Rivers, humour has always built a bridge. "I took Melissa to dinner after the shivah and she was such a wreck I couldn't reach her. I looked at the prices on the menu and I said, 'Melissa, if Daddy was alive he'd kill himself all over again.' She laughed. Rivers blasted open the shame and guilt of suicide by joking about it. At the time, the media was cruel but Rivers received letters saying: "You saved my life." Now she speaks regularly at suicide-survivor lectures.

She moved to New York and started again. Humour has been her rock. "I know in Auschwitz I'd have been making a joke as I walked in. I'd think they'd think, 'She's funny, we won't get rid of her.'" There is seemingly nothing she can't get through. But she also seems vulnerable. She admits she misses having a person you can tell everything to. "I went out with a man for nine years and that's over, and also my best friend, Tommy, died. I feel the most lonely when I'm in the country. I have this great house with five fireplaces and I can't go up there alone. There's no one to say, 'We're here by ourselves. Isn't this great?' It's horrible when you meet an old beau and they're remarried and you have to say, 'Congratulations.' You want to say, 'Die.'" She takes care of herself but wouldn't mind a man in her life to help her out. "I'd love a man to say, 'Joan, do you really want to go to Morristown [where Rivers has a show] tonight? 'Cause we could stay home and watch TV and put the fire on.'"

Not that any of this has her discouraged. "I haven't peaked yet. I swear in my heart and soul, I have not done it yet - whatever 'it' is. I know it's coming. No question. I work very hard because I love it. I don't believe in the hereafter - life should all be adventures. It should all be fun. I've been in the business for 40 years, and when they send a car for me, it's fabulous. It makes me feel special. And lucky."

Upstairs in a tiny room, there's an old-fashioned card catalogue. I stumbled upon it by accident - files with labels like "No Sex Appeal", "Annoying Habits", "Melissa's Dates" and "Tramp". There are dozens of these files, and when you pull out the drawer, there are hundreds of index cards, with jokes typed on the indexed subject. No wonder she never feels jaded: she works too hard. And comedy has been good to her. It's saved her, and held her together. "Look what's it given me!" she says, throwing her arms wide open.