For a long time, Byron Katie’s children thought she was having them on. Her character seemed to change overnight, and they didn’t trust her one bit.

For 10 years – until that day – she had spiralled into rage, paranoia and despair, becoming so depressed she seldom left her house. She’d stayed in bed for weeks at a time, and her children learned to tiptoe past her door to avoid her furious outbursts.

But one morning, when she was 43, she woke up on the floor of a halfway house for women with eating disorders, and everything seemed different.

Something in her mind had shifted, and Katie suddenly understood that all the things that had been giving her so much stress were just thoughts.

Stressful thoughts, but not reality. So she could let them go.

“Laughter welled up from the depths and just poured out,” she remembers. “Everything was unrecognisable.”

The change that came over her was astonishing. And everybody at home thought it was too good to be true.

Her daughter Roxann was particularly suspicious and used to be scared to be in the same room as her mother. What was she to make of this woman who seemed “joyful and innocent like a child, and filled with love” (as Roxann put it)?

Was it a scam? Was Katie pretending to be happy all the time, and sweet and kind? Would there be some kind of payback after a few weeks?

Not that quickly, no. In a short time, people who heard about the change started knocking on Katie’s door, asking her to help effect the same kind of transformation on them. Then she started getting invitations to meet small groups in people’s living rooms, then larger groups, in church halls, community centres and hotels.

Since 1993, she has been on the road almost constantly, bringing what she calls The Work to anyone who wants it. The “new” Katie was here to stay.

Today, on YouTube, you can watch hundreds of videos in which Katie helps people from around the world to dismantle stressful thoughts, using a line of inquiry that seems laughably simple when written down.

Just spell out clearly your stressful thoughts, she explains, then ask four questions about each thought in turn:

Is it true?

Can you absolutely know it’s true?

How do you react, what happens, when you believe the thought?

Who would you be without the thought?

It doesn’t sound like much, but it’s extremely diverting – often actually funny – to watch Katie walking people through these questions, from the brink of rage and despair to some kind of bliss, in front of a live audience.

How can that be possible? She explains: “Most people spend a large part of their life thinking, essentially: ‘This shouldn’t be happening. I shouldn’t have to experience this. God is unjust. Life is unfair.’”

Katie shows them that it’s much easier to stop struggling with reality and accept whatever is happening.

Some people adore her to the point of worship. When I told friends I was interviewing her, a few responded as if I said I was meeting Gandhi, or the Buddha. And that’s not entirely off-whack, because now Katie has published a book with her husband, the Buddhist scholar Stephen Mitchell, exploring similarities between The Work and the Buddhist Diamond Sutra.

I interviewed them together, in a recorded video call. Katie and Mitchell sat on a sofa against the same black background you can see on her YouTube videos. And Mitchell described his wife’s special talent: “One of the revolutionary insights Katie’s had is: no one else can possibly cause my problems. The only way that I can have any kind of problem or stress in this world is if I’m believing an untrue thought.

“This makes everything extremely simple. Because if the problem is with me, then the solution is with me.

“I don’t have to change anybody in my family, my children, my spouse. I can absolutely transform the situation by becoming aware of what it is I’m thinking and then questioning those stressful thoughts.”

Many people will find this hard to swallow. They might even say it sounds like victim-blaming.

But Katie has helped people do The Work on rape, war in Vietnam and Bosnia, torture, internment in Nazi concentration camps, the death of a child and the prolonged pain of illnesses such as cancer. “Many people think it’s not humanly possible to accept extreme experiences like these,” she says. But she has seen that it is. (You can watch some of those conversations online, and judge for yourself.)

Of course, most people’s stressful thoughts are more humdrum.

But that’s good, because Katie says the “teachers” we need most are the people we live with: “You can write an entire worksheet on your mother, and later find that your relationship with your daughter has dramatically improved, because you were attached to the same thoughts about her, though you weren’t aware of it.”

I ask how long it took for her family to embrace The Work. “One day, after disappearing for three days, Roxann came home and pleaded: ‘Mom, I can’t do this any more. Please help me. Whatever this thing is that you’re giving to all these people who come to our house, I want it.’”

Katie obliged. And her older son Bobby came to trust Katie enough to share something that had troubled him for years: “You always favoured Ross [his brother] over me, always loved him the most.” But instead of scolding Bobby for saying this, as she would have done in the past, Katie asked herself if what he said was true. “I’d invited my children to speak honestly, because I wanted to know the truth. So I said, ‘Honey, I see it. You’re right. I was very confused then.’”

Family life throws up constant surprises, and opportunities for stressful thoughts – about the tasks we have to do, or the people we live with, she says. We must make a habit of investigating them. It’s a process. It never ends.

“Roxann called me one day and said she wanted me to attend my grandson’s birthday party. I said I had a commitment that day in another city. She was so hurt and angry that she hung up on me. Then maybe 10 minutes later she called and said, ‘I’m so excited, Momma. I just did The Work on you, and I saw that there is nothing you can do to keep me from loving you.”

• A Mind at Home With Itself by Byron Katie (Rider, £12.99). To order a copy for £11.04, go to guardianbookshop.com or call 0330 333 6846. Free UK p&p over £10, online orders only. Phone orders min. p&p of £1.99.