The Queen of Katwe debuted a day earlier at the Toronto International Film Festival. "I never dreamed of something of this kind … especially the red carpet part," she says. "I was panicking at first when I saw it; everyone was screaming my name. I had never experienced something of that kind. But then after some time I gained some confidence…"

That word confidence is key to her story. Standing beside her were the film's A-list stars, David Oyelowo and Lupita Nyong'o, the director Mira Nair (Salaam Bombay) and the 14-year-old Madina Nalwanga, who plays Phiona. There was also the shy figure of Robert Katende, who started it all by teaching Phiona to play chess in a makeshift Katwe church in 2005. Katende's chess club has produced a couple of champions, but none like Phiona.

She was illiterate, but quick and aggressive on the board. She beat Coach Katende within a year. Then she beat the privileged kids at Kampala's most prestigious school. In 2007, she won the first of three consecutive Ugandan women's junior championships. In 2010, she competed at the Chess Olympiad in Russia – against 1000 players from 149 countries. That tournament was the focus of an article by Tim Crothers in ESPN magazine, in January 2011.

Fast forward one year. The phone rings at Nair's home in Kampala, where she has lived for 27 years. Tendo Nagenda, a vice-president of production at Disney (whose father is Ugandan) wants to come over for tea.

"We took a walk around my garden and he told me about the ESPN article, about this kid Phiona, who lived 15 minutes away in Katwe and went from a corn-seller to become a chess prodigy … and he asked me to make a film about her," says Nair. "I met her within a couple of weeks – actually in New York City, where she was playing Kasparov. I had pretty much committed to it in any case, because the story is so remarkable. I have always been drawn to stories of people who are considered marginal to society."

Nair decided to shoot in Katwe, a major logistical challenge, but she was ready for that. The film school she runs in Kampala has trained a generation of East African film-makers. Nyong'o, who grew up in neighbouring Kenya, is an alumnus of Nair's Maisha Film Lab, which Disney is now supporting.

Nair brings great joy and colour to the film, without fudging the harshness of life in Katwe. Disney backed her all the way.

"They never, not once, asked me to sanitise the film," she says. "They actually embraced the truth I was giving them.

"For me it was vital to present a prismatic view of the world. There is not just one person alone – "I'm gonna make it baby" – that sort of American individualism. It is not that … I see that everyday dignity, that abject struggle and the embrace of life around me in Kampala and I have never seen that on a screen. So it was the beauty of that challenge to consolidate what I know about our way of life and living, and culture and streets, and fashion and style, and slang and humour. And distil it into this remarkable true story of Phiona who refused to accept that she should remain in the little place she was born into."

Nyong'o plays Phiona's fiercely independent mother Harriet, who struggles to feed her four surviving children after the death of her husband. Harriet does not understand chess or the world it opens up for Phiona. She sees only a distraction from the daily struggle for food, and a man (Robert Katende) she does not trust.

Nair cast 13-year old Ugandan Madina Nalwanga as Phiona after seeing 700 girls in Britain, South Africa and all of the countries of East Africa. Nalwanga had never acted. Nyong'o says she learned fast.

"Madina is a dancer so she has this discipline of rehearsing – and she was very curious and absorbent and eager to learn. She would see me warming up and ask me what I was doing and then before you know it, she was doing it as well."

Oyelowo, who lived in Nigeria from age six to 14 with his Nigerian parents, liked that this would be an African film with a largely African-based crew and director. Too many films by Westerners show a limited awareness of the continent.

"Queen of Katwe is a film the likes of which I have been longing to see as an audience member for years," he says. "It feels radical because we haven't really seen a balanced view of what life is like in Africa."

Queen of Katwe opens December 1.