A bit sceptical: that's how I felt when I sat down one afternoon recently to draw Edinburgh Castle. Knowing my limitations as an artist, I had a sneaking suspicion I wasn't going to enjoy this.

If the assignment was daunting, the explanation on the Campaign for Drawing's website about the innate value of drawing as a "basic human skill useful in all walks of life" was just puzzling. Yet what can I say? Perhaps the cautious approach helped - but now, having spent hours poring over paper, it all makes sense.

As campaign director Sue Grayson Ford points out, children start drawing before they can do almost anything else, but drawing falls away once they start to write. It might have been different in Jane Austen's day, but nowadays, after the age of 13 or 14, most of us never draw another thing, except for doodles when we're on the phone. I gave up art when I was 13, then went through a cliched episode of sketching family members in my early 20s; luckily for them, I grew out of it. Since then: nothing.

Sitting on a bench in Princes Street Gardens, memories of art homework flood back. The habit of tortured concentration is incredibly familiar, head bobbing up and down looking at the subject and trying to reproduce it. I draw a line, rub it out, get my perspective all wrong and fret about how naive it looks. I don't notice the time passing, or the people.

The rock face becomes an obsession. I want to convey its crags and sheer cliffs, and the slightly menacing shadow it casts over the gardens below - but can't, because I lack the skill. Still, an hour later, something that looks more like Edinburgh Castle than, say, the Empire State Building has emerged on the page. More importantly, and to a surprising degree, I've enjoyed myself. For that hour, my mind emptied of all other thoughts.

A few days later, I am standing with the artist Stuart White in the Lighthouse architecture and design centre in Glasgow, looking at pictures people have made during the Big Draw - a Campaign for Drawing event which has been running throughout the UK during October, with exhibitions at 1000 different venues. In Glasgow, interested members of the public were given photocopied illustrations of various city landmarks, drawn by White, then encouraged to add their own "imaginative extensions".

So, someone has done a fabulous drawing using the Armadillo as the folds on a medieval woman's cowl; someone else has turned the Finnieston Crane into a shoe; another has made the Red Road flats into a creature from the deep. The spirit of Monty Python artist Terry Gilliam seems to be everywhere you look. The artists included children as young as seven, teenagers, students and mothers - people who'd just popped in to the gallery on a busy Saturday afternoon. It was inspiring. Suddenly, the words on the website made sense: drawing is about "observation, self-expression and fun".

For White, it's second nature. A graduate of Glasgow School of Art, he now works as an illustrator. "I keep sketchbooks that I draw in each day," he says. "It's like a diary for me: rather than write down what's happening, I sketch down."

But though he has talent, White is adamant that it's not a prerequisite for drawing. "I heard a really sad thing: that the closest people get to drawing these days is signing their name," he says. He wishes it weren't like that. "You don't have to have talent to enjoy drawing. I totally believe that everyone can draw; it makes me sad when people say they can't. I can understand why people say they can't do physics or maths, but everyone can pick up a pencil and draw."

That was also the belief of the Victorian art critic, writer and artist John Ruskin, in whose memory the Campaign for Drawing was established. "He drew almost every day," says Grayson Ford.

Ruskin saw drawing as a way of observing the world around him and connecting with it, and this is one of the ways in which it has educational value. The Campaign for Drawing has a major educational element, and has worked with 500 schools and 30 higher education institutions since 2001.

Drawing is sadly neglected as a tool for learning, says Grayson Ford. It can be applied widely at all stages in the curriculum and in a variety of ways. Drawing a scene from the Highland Clearances might be effective for learning about eighteenth-century Highland life, for example, but representational work is only one facet of drawing; others include diagrams, mind maps and annotated sketches, which are useful in maths and the sciences.

It would be wrong, though, to imagine that drawing is just for children or that its benefit is primarily educational. "There is a perception at Big Draw events that people can deliver their child and just stand back. But I'm afraid that's not allowed," says Grayson Ford. Everyone is expected to get involved, she explains - and in this way the organisers hope to boost people's confidence, plus their appreciation of how satisfying drawing can be.

For many, this means overcoming that fear of "getting it wrong". Indeed, as far as White is concerned, there's no such thing. "People have memories of drawing being graded on technique," he says. "But it shouldn't be about technique; there's no one right answer. It should be about the activity, about making mistakes' and being creative."

It is time to show him my picture. I put it under his nose, feeling as if I am standing at the teacher's desk. We discuss the rock issue. "I think they're quite expressive," he says, kindly. Criticising people's art is not something White likes to do. I have made some photocopies and tried to draw an imaginative extension - a slide down the rock, with a businessman on it - but, frankly, it is lame. And look at my trees. The willow looks like someone's wig.

"Well, why not make it into someone's hair?" White says.

And so, taking that as my cue, I go home and try again. Instead of trying to draw things to scale and in context, the picture acts like an inkblot test. From the shaded rocks, an elephant emerges; in the crags on the rock face, the eyes and beak of a bird. The willow tree becomes a hairy dog; the buttresses in the castle wall the spines on a crocodile's nose. And behind the ramparts, just for the sake of it, a cat appears. The final result? A weird mishmash that looks like it's been done by a 10-year-old. But perhaps that's the point. And in that spirit, I'm off to buy a pencil case.

How you can unleash the artist within