Visit Ali Smith's terraced cottage in Cambridge and you'll quickly begin to suspect that you've stumbled into one of her fictions. For a start, you can't quite find it as you wander up and down the street, and it's only when you spot a discreet gap in the houses that you're on the right track. Suddenly, a tiny cul-de-sac is revealed, a row of diminutive dwellings on one side, their gardens of tumbling roses on the other. There is an enchanted air, a feeling of a secret world just off to the edge of the real one, out of ordinary time. And once Smith has ushered you inside, where stacks of books and magazines wobble precariously alongside rows of vinyl, and postcards and photographs are pinned to walls, you begin to realise that there is a distinct overlap between the author, her surroundings and her fantastical, expansive, time-slipping, language-juggling books.

Those books are split almost evenly between short story collections and novels such as Hotel World (2001) and The Accidental (2005), both of which were shortlisted for the Orange and the Man Booker prizes, with The Accidental winning the Whitbread novel of the year award. In 2012, she published Artful, four essays – originally lectures that Smith gave at the University of Oxford – joined together by a fictional narrator, devastated by bereavement, who has found a slew of lecture notes left by his or her dead partner. It was a characteristically playful, genre-bending meditation on art, its origins, its nature and its uses – themes that recur across her work, and perhaps nowhere more powerfully than in her sixth novel, How to Be Both, longlisted for this year's Man Booker.

The clue is in the title. How to Be Both consists of two parts, one set in the present day, concerning George, a teenage girl whose mother has died suddenly, the other imagining a life for the 15th-century Italian fresco painter Francesco del Cossa, of whose actual biography little is known. But here's the twist: the novel exists in two editions, one with George's story first, the other with Del Cossa's. Each narrative contains references to the other, but they can be read separately, and in either order. Whether you are in the bookshop or ordering an ebook (in which case, both versions will be delivered to your device), you get to choose, or to abandon yourself to chance.

It might not be quite as radical as The Unfortunates, BS Johnson's novel-in-a-box in which chapters can be shuffled and read at random, but it's still pretty extreme. Or is it? Smith, who in conversation is as mischievous as her work might suggest, insists not: "It seems to me very simple and unostentatious." In general terms, she hopes that the book "gestures to all the ways to read that are possible", but, sparked by reading the Nobel-winning Portuguese writer José Saramago's thoughts on the subject, she was more specifically interested in exploring fiction's problem of representing synchronicity; the fact that whereas in life all sorts of things can happen at the same moment, on the page one event must precede another. "In a way that makes the novel a moral form. You have to have sequence and consequence in the novel. That's one of the reasons it's societally tied and time tied."

That preoccupation also explains How to Be Both's fascination with frescoes, which infuse both its structure and its story. "It's about fresco form," Smith explains. "You have the very first version of the fresco underneath the skin, as it were, of the real fresco. There's a fresco on the wall: there it is, you and I look at it, we see it right in front of us; underneath that there's another version of the story and it may or may not be connected to the surface. And they're both in front of our eyes, but you can only see one, or you see one first. So it's about the understory. I have the feeling that all stories travel with an understory."

This might sound like a cerebral way of making fiction, and to an extent it is: Smith began her professional life as an academic, and her doctoral work was on the importance of the ordinary in modernist literature. But her project then (as it is now), was to reclaim modernism from arid and somewhat nihilistic intellectualism: "People tend to see modernism as the opposite of a celebration. They see it as a fracturing and an art built round an absence; but it's really a celebration of our existence." In support of her theory she cites the "flourishing, beautiful poems about big-finned plants and beautiful, gorgeous, exotic animals" that Wallace Stevens wrote about Florida before he developed a "more cool, clinical thinking self, where the world has to be sidelined to thought". Thinking back to that PhD, undertaken in the critical theory-heavy 1980s, she adds wryly, "it was an unfashionable thing to want to write a thesis about, that's for sure".

But her view of post-first world war modernist literature explains a great deal about the joyfulness that pulses through her work. How to Be Both really took root in her mind when she opened a copy of art magazine Frieze, and happened upon a picture of a fresco in the Palazzo Schifanoia in Ferrara. She was immediately stopped in her tracks: "It's simply a man, in rags, who has to be one of the most beautiful men ever, and he's wearing ruined, gorgeous clothes. He looks rich and poor at the same time, like he's been ruined, and yet nothing will ever defeat this man. Nothing. It just looked to me like one of the most powerful images I'd ever seen."

She was so gripped that she and her partner, the filmmaker Sarah Wood, who provided the artwork for Smith's 2013's fiction-cum-biography Shire, rushed off to Ferrara to see them. Returning to England, she started writing a novel about something else. It was "fine". But one morning four months in, "I knew I was writing the wrong book." She put it to one side, started reading up on the Renaissance "with the eyes of a child", and tried to find out everything there was to know about Del Cossa. "I couldn't deny what it was asking of me," she remembers, "which was to go as close to a life of which there was so little left in the world, but the so little that had been left was so much."

Smith describes herself as "a really uncool, geeky enthusiast". Was she aware of the power of books from a young age? "Oh, always!" she laughs. "I was profoundly changed by Charlotte's Web. When you fall in love with a book something especially interesting and exciting is happening because of the way language works on us as human beings. And I love language. And I also love butterflies, and cloud-shapes, and types of train. What can I say? The world is a proliferation."

She spent her recent 52nd birthday interviewing the celebrated American short-story writer Lydia Davis at the Edinburgh international book festival, where she was a guest selector. Smith is not, she says, keen on public appearances, but is a notable supporter of other writers past and present, contributing introductions to forgotten masterpieces, appearing on panels to commemorate the work of, for example, Angela Carter or Tove Jansson. At Edinburgh she even elicited a rare appearance from Nicola Barker ("a genius").

She doesn't much love being interviewed either, and rarely is. "There's nothing to say! How many times can you tell the same story? There is actually nothing to say about me."

Smith grew up in Inverness, the youngest, by some years, of five children, and had what she describes as "an ideal childhood". Her parents had both left school prematurely, thrust into the world of work by the death of their parents and a shortage of money. Her mother emigrated from the north coast of Northern Ireland and became a clippie on the buses up and down the Moray Firth; when she was old enough, she joined the WAAF where, one day, a pair of electricians came to rewire the bedrooms. One was Smith's father. She captured their meeting in a short story entitled "The Story of Folding and Unfolding" – "there's not much that's autobiographical in my work but that one is" – which described her dad's mate opening all the lockers to look at the girls' underwear. Her dad, passing by, saw one in which everything was beautifully folded. "So my dad went, 'Who's is this?' And he looked at the name on top, and he said 'I'm going to meet this girl'."

Her father founded a small contracting business, wiring up the houses that lined Loch Ness, including that of the writer of Ring of Bright Water, Gavin Maxwell ("He's a bit funny, you know," he told his daughter). Deprived of education themselves, they determinedly steered their children towards university, with the professions firmly in mind; Smith was to be a lawyer. "I knew I'd be terrible. I couldn't argue to save myself, never mind save anybody else, and I knew there was something else I wanted to do." She wanted to study English; her parents didn't want her to. But there was never a row: "In a family of five, you learn to sit still as a stone sometimes, and just hold your position … there was a pressure and I exerted a similar pressure back, and at some point it was all right."

She went to Aberdeen, got a very good degree and eventually ended up in Cambridge doing her PhD, which led to a teaching job at Strathclyde. It was here that life began to unravel in all sorts of ways: her mother died after years of poor health; Smith was working exceptionally hard and, at the age of 27, she developed chronic fatigue syndrome, from which it took her many months to recover. She likens herself to Woolf's description of the ill person as "a blown leaf on the edge of time"; she says now that "I had to stop so that I could decide which road to cross".

At the same time, academia was turning itself into a business: Smith recalls being told to call her students clients, and being unable to learn all the names of the students in her overcrowded seminars. The subject of education is one that rouses her to anger and dismay: "Neither of my parents had it; we all had it; and now people can't have it again. What are we doing in the world that we are denying people the right to an open education? And we are denying it by making education something you have to pay for so drastically. How are people supposed to afford this? How? I was the last of a lucky generation. We were given education so fully, so openly and so freely. Why is our generation doing this to the people behind us?"

But academia's loss was to be literature's gain. Smith and Wood moved back to Cambridge and, still recovering, Smith began to write "story-shaped things", at first "just getting my arms to work again. It was as physical as that." She says she doesn't know what she was trying to do in that early work. "I was just interested in the notion that a story could take lots of shapes." She speaks of it as "a very energetic form, so full of the brevity of life. It's so about mortality, it's so about over-ness."

Since her first collection, Free Love and Other Stories, was published in 1995, she has tended to alternate between the long and short forms, seeing the story as free where the novel is tied to class and to time: "The novel is always in one way or another a clock. The minutes will go round. You start here and you end up there." Except in her new book, surely, where you can start and finish where you like? She bursts out laughing. "I know!" And then considers: "But actually you do, you see, because whatever way you read this book, you're stuck with it. There are two ways to read this novel, but you'll end up reading one of them."

Whatever their form, Smith's fictions return to certain themes – duality, love and its loss, time and its passing, how we can find one another – blending them with political concerns such as the enterprise culture, mechanised warfare and the rise of surveillance. Wordplay abounds, as do collapses in time, moments of metamorphosis (a woman with a rose bush sprouting from her chest), shifts in gender; there is a bringing together of the fabular and the quotidian that is both uncanny and strikingly fertile.

Children are frequent characters in her work and often, too, there is a mysterious stranger: Amber, the woman who turns up uninvited in The Accidental, or There But for The's Miles, who locks himself in a bedroom during the middle of a dinner party and refuses to come out. These figures are often deeply disruptive, and always narrative catalysts. Who are they? "If we look at the larger story that the world is telling at the moment in its horrific mayhem, it's that we are drawing more and more borders, we are more and more fearing the notion of the outsider or the stranger. She says The Accidental is really about what you do when the person who is from the outside knocks on the door of your house. "Do you let that person in or not? And what if, as in all the fables and myths, that person is the gods? Or what if that person steals everything from you? Or both? We have to remember hospitality. We have to remember what it's like to be humans, to be strangers in the world and be welcomed in."

A great lover of Greece, she remembers talking to a friend there as the financial crisis began to grip. The woman told her that she feared the Greeks were losing their gift for friendliness, their "love of the stranger". It strikes me that this is exactly what Smith's book is about: a way of bringing to life what binds us, and of making an art that will allow us to understand that. "In all our individual states," she says, "we are always communal. There is always a point where a hand reaches out to another hand."