Hidden away under Edinburgh, a dedicated band of experts are working their magic to ensure that our literary heritage, like JM Barrie's Peter Pan, never grows old

A first edition of Peter and Wendy, JM Barrie's novelisation of the play about the boy who wouldn't grow up, is lying on the table in front of him, and the 50-year-old conservator, who has worked here for an astonishing 35 years, is constructing a delicate bespoke stand for it. Next to him lie a pile of similar first-edition books by Barrie, as well as some rare and fragile-looking manuscripts, the collected value of which would probably have most insurance men rolling their eyes in horror.

"You can't think about the value of what you're handling too much, to be honest," says Yeoman as he gently places the book onto the stand. "Otherwise you'd start to panic."

Welcome to the Conservation and Preservation Department of the National Library of Scotland. Tucked away deep below the hallowed halls of the nation's public library, it is the engine room of the organisation, a sort of A&E department for books and manuscripts, which uses a dazzling array of traditional methods to restore ancient literary masterpieces to their former glory.

Everywhere you turn in this vast workshop there is a rare gem: here a box of miniature Shakespeare plays, each one no bigger than the size of a thumb; there, a lightbox as big as a shop window used for treating large maps that have suffered some damage; here, a collection of stamps, or pallets, used for the process of gold-leaf embossing.

The National Library receives 300,000 new items every year. The full collection stretches to a massive 14 million, and it is growing every day. Conservation manager David Kerr estimates that around 5,000 items are awaiting treatment by the department at any one time, meaning the five staff in the workshop, as well as a further four based at a secondary site at Sighthill, are extraordinarily busy.

"Material often arrives to us in very poor condition," says Kerr. "They come from a wide variety of sources, either they've been purchased by curators or donated to us."

When any new book or manuscript arrives in the department it is immediately classified. A "C" classification generally means it comes from the 20th century, and "AA", means it is particularly precious, and often several hundred years old.

"We don't particularly put value on the collection in a financial way, but we're going to spend more time working on an 'AA' than, say, a 'B'," says Kerr.

Over in one corner 34-year-old conservator Kate Kidd is currently working on re-sewing an old volume about the artist John Turner, using cords, linen and thread. It is an intricate process, but one that, says Kidd – who studied book conservation at Camberwell College of Arts in London – is actually "quite simple".

"This process has been around since books were first invented, when they first moved on from scrolls," she says. "There are different methods – you could use linen tapes or vellum tips. One of the most important things is that all our repairs need to be reversible, so that 100 years from now, if another conservator comes along, they can undo what I've done."

Kidd admits that one of the biggest distractions of the job is the temptation to read everything that you're working on. When the John Murray archive arrived at the library she was assigned to it as its dedicated conservator, and worked on many of Byron's letters.

"I'd love to be able to sit and read everything but you just can't," she says. "Because the John Murray Archive has a large collection of correspondence, you do realise this person sat down and wrote a letter at a desk. It brings the history alive and it does make you feel a connection with what you're working on."

Kidd's personal favourite item that she's worked on is the commonplace book by Caroline Lamb, a lover of Byron: "It's a book in which she'd write all her thoughts and musings and lots of little sketches.

"I did a full treatment on that, completely disbound and cleaned all the pages and completely rebound it so it's now safe to handle. Hopefully that will keep it for the rest of its life and that's a really exciting thing. It was an amazing item to work on – she poured out all her thoughts and emotions onto those pages."

In fact, Lamb's book was one of those damaged just over a year ago when the library experienced a serious flood that damaged around 1,000 books and manuscripts in its collection, after a sprinkler pipe failed, causing 5,000 litres of water to run through the building.

"The Caroline Lamb book was probably the most significant item to be damaged during the flood," says Kerr. "But Kate conserved it afterwards, and it's actually in better condition now than it was before the flood."

Kidd's use of the traditional resewing method is one of a range of traditional processes carried out in the workshop. Kerr shows me one corner of the room dedicated to gold leaf. It is a long and delicate process, involving laying small pieces of gold leaf on a small stool made of reverse leather and then, curiously, using the grease from one's own forehead to help the gold leaf stick.

"We use the gold leaf for putting titles on books," says Kerr. "We use small pallets with different typefaces and different styles, and you need to use a small stove in order to heat them up." Although the workshop deals primarily with books and manuscripts, it does occasionally handle larger items.

Kidd remembers having to put an ancient dead and stuffed turtle from the Galapagos islands – part of an exhibition on Darwin – into the freezer for several weeks in order to kill off any nasty beasties that may have been lurking inside it, while Yeoman confesses that when one of Winston Churchill's original hats came through the department a while back, he couldn't resist the temptation to (carefully) try it on.

Yeoman, who has worked here since he was just 16, has seen countless treasures pass through his hands over the years. Some, however, are particularly special. "I'm a huge fan of Robert Burns and getting to hold the original Auld Lang Syne, and knowing that Burns touched it, that was pretty special," he says.

He's also been fascinated by some of the more modern items the library has dealt with. Not long ago, he was dispatched to London to pick up a first edition copy of JK Rowling's The Tales of Beedle the Bard – worth 1million. Putting it through the airport scanner was, he says, a hold-your-breath moment.

"Security asked me what was inside and if they could have a look," he says. "I said that they could, but not in front of all the other passengers."

Fortunately, the book made it back in one piece. "A day or two later I saw JK Rowling reading from it in the Signet Library. That was fantastic to see."

Upstairs, some of the conservators' hard work is on show to the public. The Library is currently running an exhibition on Scottish theatre, with items including a three-piece gold costume worn by actor Alan Cumming in a staging of The Bacchae, and the original set for The Cheviot, the Stag and the Black, Black Oil – a play by John McGrath – which was designed by artist John Byrne and features an enormous ten-foot tall pop-up book. Both items have, of course, passed through the workshop – Yeoman worked on the stitching of the pop-up stage set, no mean feat given its size and weight.

But quite often it is the small, hidden processes that are the ones that have the most effect on the materials the staff are working on, whether it be removing acidity from paper itself, or even very carefully and gently washing and cleaning ancient pieces of paper.

Before I leave, Yeoman shows me another part of the Barrie collection, a pamphlet containing a rare Barrie play called Caught Napping, printed in 1883. It is one of only three in the world.

"Somebody stuck a barcode on it," he says, shaking his head. Then he shows me the page. "Can you see where it was?" But, of course, there's nothing there at all.

Curtain Up: 40 Years of Scottish Theatre, runs until 3 May at the National Library of Scotland, George IV Bridge Building, Edinburgh. Admission is free.