Just inside the front door of my childhood home I have, I tell author Joshua Foer, placed a glitter-covered eyeball with cartoon legs and a long grey beard. He thinks for a moment before replying. "Is the long grey beard coming out of the thigh? That would make a lot more sense." He is right. Today, Foer is tutoring me in how to remember poetry, and the sparkling eye-beard monster is my mental cue for the line "By thy long grey beard and glittering eye".

"The whole art of this sport," explains Foer, wrapping the word sport in qualifying air quotes, "is in transforming information that's unmemorable into imagery that's so weird and raunchy and smelly and emotionally resonant that you can't forget it."

Our goal today is to commit to memory at least the first part of Coleridge's Rime of the Ancient Mariner. We are out in Embankment Gardens in central London on the north bank of the Thames where the fresh air, so the theory goes, will sharpen our concentration, and the distinctive surroundings – the statues, ponds and potted plants and the looming presence of the Savoy hotel – will combine to make the lesson itself more memorable.

Foer's book Moonwalking with Einstein documents his transformation from forgetful young science journalist to US national memory champion. With less than a year's training, he learns to log the order of a shuffled deck of cards in less than two minutes, to remember the full names of a whole horde of strangers, and to swiftly recall long strings of random numbers. Along the way he meets the world's worst amnesiac, Kim "Rain Man" Peek, and a colourful cast of international mental athletes reinvigorating the lost art of remembering everything.

It is an art that is easily learned. At least in theory. First, each item to be recalled is transformed in the mind's eye into a rich and unique mental image, replete with its own taste, smell and feel. These images – the most memorable of which are often lurid and depraved – are then deposited in order in the nooks and crannies of a memory palace, a sort of mentally constructed store room. The best memory palaces are places already rich with associations, which is why first-timers like me normally begin with their childhood homes. By tracing a certain path around these surrealist museums the mnemonist can, with practice, recover thousands of images – and with them, thousands of memories.

The memory palace method is based on the observation that the power of our spatial memory far exceeds that of our capacity for numbers or words alone. You have likely already forgotten, for example, the line of poetry I was trying to commit to memory in the opening paragraph. You should be able, with very little effort, however, to recall the layout of every house you have ever lived in, and even friends' houses or hotels you visited only once many years ago. Hence the palaces. The lurid images are almost self-explanatory: the weirder the mental picture, the harder it is to forget.

There are, says Foer, two schools of thought on poetry. "One strategy is the super-duper meticulous one used by a lot of the European memory champions. Gunther Karsten, the German memory champion, would literally turn every word in this poem into its own unique image. He might as well be memorising the VCR repair manual." For our purposes, Foer recommends the alternative – to create a single image as a mental cue for each line. This method, he points out, also requires us to understand at least a little of the poem itself.

I am, I tell Foer, having trouble with the third stanza. ("He holds him with his skinny hand/'There was a ship', quoth he/'Hold off! unhand me, grey-beard loon!'/Eftsoons his hand dropped he.") I have, perhaps a little ambitiously, tried to store all four lines in the kitchen fridge. The door handle I have removed and replaced with the gnarled hand of an old man clinging tight to the sleeve of a wedding guest's grey suit. On top of the fridge is a stuffed raven in a miniature wooden warship, while on a shelf inside, a bearded duck is biting a stranger's hand off. This is not what Coleridge had in mind.

It also seems to be making those lines, if anything, twice as difficult to remember. I ask Foer to show me how he would do it. One by one, I read him a line and he weaves an image for it, using our surroundings as a makeshift memory palace and tying each picture to a spot on the ground around us. "When I see 'He holds him with his skinny hand', I'm actually making that gesture." He thrusts out an arm, catching an imaginary stranger in a vice-like grip. "If you can engage the kinaesthetic memory, that can only help." And the ship he quoth? "I might put some big floating quotation marks around the ship."

Hold off! Unhand me, grey-beard loon! "Hold off? Hmm. So I'm going to picture a big hole over there. Just to start that sentence off. For grey beard loon, I'm going to see the guy with the grey beard and I might actually have him holding a balloon." And eftsoons? "A big letter F."

Learning poetry, says Foer, along with shopping lists and speeches, is one of the few practical uses of the memory palace technique. "This stuff was invented for oratory. That's what Cicero used it for. The phrase 'in the first place' – that's a vestige from when people used to think about rhetoric using these techniques." Rhyming poetry is particularly easy to remember. "The rhyme and the metre provide a kind of structure that basically remembers the poem for you." Free verse, on the other hand, "is a total bitch".

Cicero was, in fact, far from the first to use the method. The memory palace has been around in one form or another for at least two and a half millennia. Invented, legend has it, by the poet Simonides of Ceos, it was once a cornerstone of ancient Greek academia. Right up until the advent of the printed word an educated man was expected to convert his brain into a vast library of memorised literature.

It was not just western cultures that made use of memory techniques. "It's actually a really sad story," says Foer. "The native American Indians told their cultural epics by tying them to pieces of the landscape, so when they had their land taken from them by the US government, they lost not just their land but their history."

Now, with the almost universal availability of what Foer calls the "externalisation of memory" (chief culprits: the pen, the printing press and the web) the technique of cultivating a miracle memory is the preserve of just a few hundred "mental athletes". Though he once walked among them, Foer writes about his fellow mnemonists with a wry ambivalence. The contestants at your average memory contest, for example, he describes in the book as "overwhelmingly young, white male juggling aficionados".

Foer's own tutor and spirit guide is introduced in the book as "the mop-haired, cane-toting English mnemonist Ed Cooke". Cooke is one of just a few dozen Grand Masters of Memory, a title that he earned at the age of 23 by recalling 10 shuffled decks of cards and 1,000 random digits in an hour. "Ed is superior to me in the poem memorisation. And everything, really," laughs Foer.

Grand Master Cooke shares his wisdom in a hurried conference call. "One thing I'd say about the poetry is that it's always a mess until you sleep on it. I'm always astonished when I try to learn poetry and discover the next day that I have." Now in his late 20s, Cooke has memorised large chunks of Milton's Paradise Lost, at a rate of 100 lines an hour. In his book, Foer describes his mentor's brain as a vast metropolis of memory.

I ask Cooke where he found enough mental space to store Milton's epic. "I used anything and everything," he says. "I've used all sorts of parts of London, so I've got one bit that's in St Pancras station, I've got areas of my old school, lots of bits of Oxford and friends' homes and so on. I'd be jumping from an internet cafe in King's Cross to a small house in Wiltshire."

The poem is spread so diffusely across the warehouses of his mind that he sometimes temporarily forgets a fragment because he just doesn't know where he's put it. "It actually took me a bit of detective work to work out where it was all stored." Before he goes, I ask Cooke if he ever worried that his protege would surpass him. They both laugh. "No," he says. Then he's gone.

So what use are the secrets of memory to the rest of us? Could they revolutionise education? "It's not my mission in life to transform education or anything like that," says Foer. "But I wish somebody had told me about this in high school, because there is a load of information that you are asked to memorise. If there are more effective ways of doing that, then by all means why wouldn't you? It is worth teaching kids how their memories work – if for no other reason than because it can make learning more fun."

In the book, Foer meets teacher Raemon Matthews, who trains pupils at his school in New York's South Bronx in memory techniques and mind-mapping, and brings a cohort of 12 students each year to compete in the US Memory Championships. His class is known as the Talented Tenth, after a 1903 essay arguing that an elite few African-Americans would lift the entire race out of poverty. Not one of his students has ever failed in their state exams, and the vast majority score in excess of 90%. It is a chapter that could have been a book in itself.

Exams aside, I ask, of what day-to-day use are these techniques? "One place where I always try to do this – if for no other reason than to keep in shape – is when I go shopping." Apart from that, says Foer, they are of more use to his wife, a medical student, than they are to him as a journalist. "It's not so useful to be able to remember a deck of playing cards outside of Vegas."

So where now for the memory men? "Many people who compete in this sport harbour an illusion that it will one day be an Olympic event," Foer says. He, clearly, isn't one of them, but he doesn't rule out a resurgence of interest. "I can imagine it becoming bigger than it is. There's something powerful about watching people engage this very primal capacity in a way that's kind of mind-blowing."

It is now nearly a week since my masterclass and after a little practice the chimeric denizens of the Rime of the Ancient Mariner are firmly encamped in the house I grew up in. The glittering eye – its beard now correctly attached to its thigh – has been joined by a dead sailor clutching a contract ("The mariner hath his will") and a man trying and failing to bite his own backside ("He cannot choose but hear"). I can comfortably rattle off at least the first two dozen lines, and with enough time and effort I'm confident I could build palaces to house the rest. I won't – because I have a) Google and b) other things to do – but it is just a little bit inspiring to know that we are capable, as Foer puts it, of remembering how to remember.

Moonwalking with Einstein, by Joshua Foer, is published by Penguin.