At 14 Albert Espinosa was a typical football obsessed teenager. He lived with his engineer father, housewife mother, sister and brother in Barcelona. "Like all adolescents," he tells me, "I hated my parents."

Then one day medics found osteosarcoma – a malignant bone tumour – in his leg. His chance of survival, his parents were told, was just 3% – odds so bad they were advised to take their son on holiday somewhere sunny and enjoy the last month of his life. The family packed up and set off for Menorca. "We got as far as the airport," he says, "before we decided to turn back and fight to overcome it."

For the next decade Espinosa endured gruelling chemotherapy, had his leg amputated, lost a lung and had part of his liver removed. He made intense friendships, and watched 22 fellow cancer patients, often teenagers, die from the disease. Yet, extraordinarily, he remembers it as a happy period. By the time he was finally cured at 24, he had written a book, El Mundo Amarillo (The Yellow World), not about how to survive cancer, he insists, but about how to live.

The book, which is being published for the first time in the UK, details the discoveries he made during his illness – including how to stay in touch with your inner 14-year-old, or contemplate your own death – which he believes can apply to life outside hospitals. The tone veers from humorous to just plain odd; one chapter is dedicated to the delights of "positive wanking" (proving perhaps that it is possible to be too in touch with your inner 14-year-old). A word-of-mouth sensation, it has sold more than a million copies and been published in 20 other countries.

Now devoted readers send him thousands of emails a day, and some go further: he proudly shows me pictures on his mobile of women who have had quotations from the book (such as "Trust your dreams and they will come true") tattooed on their bodies. One has it in a large font, across her chest like a necklace, another in a trail down her spine.

Espinosa, 37, also wrote a Spanish television series, The Red Band Society, based on his hospital experiences. It focuses on the friendships he made in hospital with other young cancer patients (they formed a gang called the Eggheads). He tells me that the series and the book have prompted a 48% increase in visitors to children's cancer wards in Spain. Now it is being remade by Steven Spielberg for an English-speaking audience.

They may not have had a normal life, he says, but they soon lost their fear of death and knew how to have fun. "We didn't have motorbikes but we had wheelchairs. We couldn't go to discos but we had five floors of a hospital to charge through."He recalls the time they behaved as though they were ill was at Christmas, during visits from footballers, when the child who looked the most sick would get a present. "My best acting achievement is getting a signed football from Gary Lineker," he says mischievously miming his sickbed look. "You have to put your head on the pillow and half close your eyes."

When I ask him whether he ever felt like giving up, he says no, because the gang "had a pact that if one of us were to die we would share out their life". Each made a list of the wishes they wanted to fulfil if they recovered, and when a friend died, the others would try to carry them out. Today, he says, he has the responsibility for living not just his own life, but the desires and dreams of 3.7 of his friends: "Bit by bit, I am trying to fulfil them."

His own wishes helped him too. When he was finally told he was cured, he spent a year carrying them out as a way of discovering the kind of person he had become: "The 14-year-old had goals and desires he never fulfilled, and the 24-year-old didn't know what his desires were." He refuses to tell me what was on that list: "They were dreams a kid had. There were some very crazy things. I got into trouble."

It was not just other patients who helped him to cope. Quirky advice from doctors has made it into the book too. In one chapter he explains how when he was told, age 15, that his leg would be amputated, his doctor advised him to throw a party for his limb. So the night before the operation, Espinosa gathered those "who had some sort of relationship with my leg": a girl he played footsie with; a boy whose dog had bitten him as a child; and a "goalkeeper who let in 45 goals from me in one match (well, OK only one, but I invited him anyway)". Later he danced, over and over to the same song, with a nurse. It was the party of a lifetime, he says.

Such encounters showed him the importance of friendships. He believes the intensity and nuances of different types of friendships has been ignored and the crux of his book is advising his readers to actively seek out people who can change their lives. "Over the course of time the idea of family has changed, the idea of society has changed, but our ideas of friendship have stayed the same. It seems ridiculous to me."

These people he calls "yellows" and much of the book is taken up with peculiar tips on how to recognise and approach them. But would he walk up to strangers in the street and ask them to be his "yellow"? Yes, he says, because he likes to provoke people into interacting with him. But it doesn't always go to plan: "When I go through security at airports and they ask me to explain my prosthetic leg, I say: 'I will tell you, if you tell me something about your life. Maybe something's wrong. Are you having problems with your wife?'" Does it work? Not exactly, he admits, he has been arrested twice. But he has made many friends along the way. "When you lose something, you always win something," he says, cheerily.

• The Yellow World is published on 1 November by Particular Books, £16.99