It's 2007, and the age of discovery is over. Tourists have invaded every corner of the planet and professional exploration is all about sponsorship and fancy kit. Right? Wrong, says Robert Twigger. In fact, DIY exploration is in rude health and cheaper than it's ever been. What are you waiting for?

Robert Twigger studied Philosophy at Oxford University and Martial Arts with the Tokyo Riot Police. He has won the Newdigate prize for poetry, the Somerset Maugham award for literature and the William Hill Sports Book of the Year award. He has caught the world's longest snake; was the first person to cross Western Canada in a birchbark canoe since 1793; and has hunted for lost oases in the Sahara and bona-fide Zombies in Haiti. He has written five books, made several documentary films and lectured around the world. He has a wife and two children and divides his time between the Middle East and Europe

I grew up imbibing the idea that the world was all explored. It's encouraged by watching too much television. In one evening you can easily get the impression you've gone right round the globe. Or even twice, if they're repeating Michael Palin. When I finally did start travelling I was always comparing it to television – I remember thinking in Borneo this jungle isn't half as noisy as the one I saw on David Attenborough. Take Machu Picchu. The American explorer Hiram Bingham was the first European to discover the extraordinary Inca ruins in the Andes in 1911. Travellers started making their way there in the 1950s and 1960s. Now every tourist who goes to Peru gets dragged up the mountain to view the site. Exploration is dead. QED.

Or is it? There are vast parts of the world that very few people have ever visited, or will ever visit. There are many places, in jungles, deserts and mountainous regions where the DIY explorer can be the first visitor to that precise spot. And if not the first person, the first one to write anything about that place and take a photograph. Observe it, look at it, walk through it. That's exploration.

I've recently been to the Gilf Kebir, an area the size of Switzerland in south-west Egypt with no water at all. Tourists travel with military escorts and it takes a week of desert travelling to get there, so very few do. However, imagine tourists going to Switzerland and only visiting Berne and Geneva and then scooting back home. That's what the Gilf is like – the tour groups visit two sites and then leave. We, however, stayed longer – on my last trip we discovered an ancient burial site and a new route on to a plateau unmarked with any tracks – we were the first Europeans here for sure, and possibly the first people since the rainy period in the Sahara of 7,000 years ago.

This example is replicated throughout the world. In Borneo I went to a village on the Kalimantan/Sabah border. Tourists had just started visiting – a few plane loads every year. The last anthropologist had just left– it was the dawn of a new era. But when I started making longer and longer trips with local Lundaiya hunters I began to find myself beyond the area that tourists, on their tight schedules, or anthropologists, with their village-based agendas, visited. I discovered a line of menhirs stretching right across the tribal territory and into Kalimantan. No one had written about these before, or photographed them. It was incredibly exciting. Suddenly I was an explorer.

Just because we've flown over everywhere in a jumbo jet doesn't mean we've explored it. Just because tourists queue up to gasp their lungs out on Kilimanjaro doesn't mean there isn't exploring to do on the other side of the mountain.

Actually it's the growth in adventure tourism that has sparked the recent surge in DIY exploration. Adventure tourism is still tourism but it happens in remote enough places that you suddenly see the potential. You start asking the guides, "Has anyone climbed that mountain? What's through there? Where does this river start?"

Tim Cope, a young Australian explorer, first experienced the unexplored possibilities of Siberia while on a bicycle trip across Russia. He then went back and made the first descent of the Yenisey river in Siberia, all 4,500 km of it, in a renovated rowing boat he was given for free.

I started making jungle expeditions in the late 1990s to try to find and film the world's longest snake. These trips, all over Malaysia and Indonesia, taught me that the biggest lie in geography lessons is that the world is all explored. The world is not a static place: politics, economics and natural forces change it all the time, close some areas and open up others. Even global warming has changed the nature of exploration – especially in the arctic, where daring forays by sailboat along the North-West Passage are now more achievable.

In 2005, a new cave so vast that two helicopters could fly through was discovered deep in the Venezuelan jungle. In it was also found a new species of "poison dart" frog. If you extend exploration to include bio-exploring we are still in the subject's infancy. The prominent writer on biodiversity Edward O Wilson believes that 90 per cent of a potential eight million species of insect remain undiscovered.

Retracing an old explorer's route is another form of exploration: by noting similarities and differences you explore how the world has changed over time. Starting in 2002, I made a three-season trip through northern Canada, following exactly the 1793 route of an explorer, Alexander Mackenzie. At one point, after lugging our birchbark canoe over beaver dams and rapids, we arrived at a place that was absolutely unchanged since his description 200 years earlier. There was even a mile-long log jam just as he had written in his journal. It was greatly satisfying to know that 200 years hence the place, guarded by mountains and steep impenetrable bush, would most likely still be unchanged. Just one visit every two hundred years: that was enough.

Even being somewhere 10 years after the last visitors feels like exploration. On the Canada trip I found a paddle left behind by an expedition that had been made in the previous decade. It's only finding recent rubbish that makes it feel like tourism.

Exploration is about recording an environment with fresh eyes – either because no one has been there for a long time, or because you have a different perspective. Recently I started micro-exploring England in a tiny kayak along its narrowest streams and least-visited rivers, places where no other boats can go. Suddenly the utterly familiar becomes a lost world of wildlife and new discoveries.

DIY exploration is fuelled by cheap flights and cheap gear. Getting to the zone of exploration used to be the biggest cost – now it's negligible. Gear used to be highly specialised with a price tag to match. Now that every cub scout wants a four-season box-baffle sleeping bag they are relatively cheap – the price hasn't really changed in 20 years.

Second-hand gear is even cheaper: the jungle explorer Tahir Shah buys all his Zodiac inflatables from Loot classified ads and feeds his jungle porters on Pot Noodles. DIY exploration is about using what works rather than what the gear companies want to sell you.

The only barrier to taking part in the DIY exploration movement is psychological: have you the courage, initiative and knowledge to get out there and do some exploring?

One of the first things you need is a good alibi – an excuse to be there. Tourists have the lame excuse of wanting to see something that has been photographed a thousand times before. Travellers want to see something they saw in National Geographic. Explorers want to photograph something that will appear in next year's National Geographic.

The right alibi must be sufficiently exciting to inspire you and get you into new country, or old country in a new way. For my desert exploring I settled on the idea of searching for Lost Oases. It had a mythic power as well as practical consequences. I was able to investigate all the competing theories about myths for Lost Oases while visiting the supposed sites myself.

But the real exploring is always on the back of the alibi. I found Stone Age tools, Second World War trucks, intact pottery urns and "water mountains " where ancient caravans stored their water. I found long- lost camel trails, engraved rock art, camel saddles left behind by Tebu tribesmen 100 years ago, an ancient hunters' cave beside a flint-knapping station.

It took a long time to get to base camp, so to speak. I have just spent the past two years living in Egypt making vehicle, camel and walking expeditions into all parts of the Sahara desert. It took ages to work out the basics. Places to get fuel and wood, where checkpoints were, who to trust, what maps were reliable.

It was a largely psychological problem: I didn't know where to start and there was no one there to help me. Cars were expensive and even when I got one suitable for the desert, it was hard to find people who had enough time and the inclination to visit the really remote places. Camels were another option but I had heard horror stories of unknowing foreigners being ripped off by crafty Egyptian camel men. I slowly accumulated information and experience but I had yet to make a journey that felt like exploration. For me that feeling comes from cracking some travel problem that has kept others out.

A few years before, crossing the Rocky Mountains, I found myself in a place that had defeated several expeditions before ours. The problem was the intense cold of the glacial streams we needed to wade through up to eight hours a day while manhandling a heavy canoe. As I had no one to tell me what to do I went back to my limited experience of fishing. Wetsuits were too bulky to carry but stocking-foot chest waders weren't – and being made in China, my favourite country, they were exceedingly cheap. Wading all day in the icy water was no longer a problem. A very simple solution but without it the expedition might have failed.

With the desert the problem was how to carry water without the encumbrance, limitations and costs imposed by cars and camels. I went back to my experience of dragging a canoe through the wilderness. Why not drag a sledge through the sand? No need for expensive cars or difficult camels. The friction would be too great for a sledge but a wheeled vehicle, I tentatively named, in a moment of appropriate silliness, the Advanced Recreational Sand Explorer, or simply "the trolley", might work (see photograph, page 19).

Being in Cairo it was very easy and cheap (£28) to have the sturdy prototype built. By now I had discovered that other hardy souls were joining me in using the wheeled cart as a DIY desert-exploration device. In 2006 Lucas Trihey crossed Australia's Simpson desert in 17 days using an aluminium cart, while two Germans traipsed through the Gobi tugging a hi-tech trolley with mountain-bike wheels.

The "trolley" was created in the true spirit of DIY exploration, the same spirit that has carried Jason Lewis around the globe by pedal- powered boat and John Harrison in a folding canoe up unexplored tributaries in Brazil. Go back to basics and try anything that looks like it might work. Instead of killing your enthusiasm with endless phone calls to potential sponsors, reduce your costs with an ingenious bit of homemade kit.

The "trolley" got me out into the desert. Two weeks' worth of water and supplies for a team of two could be carried on it. At last I felt I was really exploring, going where there were no vehicle or camel tracks and filling in the gaps in the old 1941 survey maps. After making several trips I met Arita Baaijens, Holland's leading desert explorer, a female Thesiger if ever there was one. She had made long solo camel trips through Egypt and Sudan before the advent of GPS. Talking to her was another turning point. I began to see that camel journeys were not as expensive or difficult as I had earlier imagined. Arita introduced me to Bedouin camel owners and I began to learn about this most traditional way of exploring the desert.

I knew there was huge groundswell of people eager to take part in real exploration when I wrote an article about searching for new examples of rock art in the desert – I was inundated with requests to join the expedition.

But instead of just another touristic holiday, I had a vision of being able to give people the basic knowledge and experience, while on a real expedition, to be able to do it later by themselves. I had reported for magazines on adventure-tourist trips and I saw how the "clients" were made dependent on the tour leaders and their assistants. They were kept out of the kitchen on spurious "insurance" grounds (really because they got in the way). They were denied the chance to help pack vehicles because that might slow things up. But people want to learn. On one trip I accompanied, an Italian woman showed me a lone GPS point that she'd copied into her notebook. Never mind that she'd never visit that spot again. For her it was a proof that she was involved in a real expedition.

I saw that the skills I had learnt over the past few years could easily be taught to someone directly. It was no good learning about the desert from books. I'd done that: you had to experience it. From this came the idea of the Explorer School. Research into team learning has shown you pick things up fastest on the job – and not in the classroom dissecting the lesson before and after the experience. At the Explorer School we've put all the core skills you need to make a desert expedition by camel into a two-week journey of real exploration in one of the least frequented parts of the Egyptian Sahara. You'll learn navigation by night and day, survival skills, water management and expedition planning. From our Bedouin teachers, you'll master skills in packing, loading and managing camels, cooking bread in hot sand, reading tracks and avoiding the worst effects of sandstorms. Where we go the maps are just white spaces so we'll teach you to make your own. Every expedition follows a new route so you'll be going somewhere you, me and even the Bedouin have not been to before.

Most people with jobs do not have the time to be able to do the groundwork, the reconnaissance. So they opt for tourism – which is a pity. But at the Explorer School we've provided a new option by condensing and focusing all the skills you will need to become a real explorer yourself.

The future of DIY exploration has never looked brighter. The collapse of communism has left most of the world open, with a little ingenuity, to any would-be explorer. New materials and hybrid thinking are generating new ideas all the time. The mega-transect concept pioneered by Michael Fay, where the object is to log wildlife along a journey that aims to avoid all human settlement, has resulted in some interesting new journeys. Satellite phones have brought previously expensive communications capability to anyone with £500 to spare. Weird new vehicles can take you to places previously thought inaccessible. Super-wide tyres have been fitted to a mountain bike for an attempt at reaching the South Pole, powered hang gliders have been used to ferry gear over rapids in the upper Nile and ultralight pack-rafts have opened up new vistas in mountain-range and lake exploration. There is also a growing appreciation of the transport skills of indigenous people. Long journeys are waiting to be made by explorers using only traditional means – be it seal-skin umiak or claw-sailed catamaran. The internet has become a resource for non-corporate sponsorship and the cheap cost of video has lead to new ways of publicising your travels, even without the help of National Geographic.

Adventure tourism has its own logic for keeping the punter ignorant – they'll come back again and again, ignorant bunnies lining up for another thrill ride. No thanks. My ideal client is someone I see once and never see again. Someone I only read or hear about, a person who has made their own expedition somewhere on this vast and undervisited planet.

Robert Twigger can be found at theexplorerschool.com

Robert Twigger's Top 10 places to explore for yourself

1. Interior Labrador, Newfoundland. Very remote, even now, and kept remote by an inhospitable climate: bugs in the summer, ice in the winter.

2. Sahara – anywhere where there is no oil, which is most of the southern desert.

3. Antarctic islands off Graham Land coast, particularly Anvers, Adelaide and Alexander islands.

4. Remote Tepuy – huge rock mesas that rise out of the jungle in south-eastern Venezuela, the most famous being 'The Lost World' of Conan Doyle, which, though often visited, still has unexplored sections.

5. The Sudd swamp – the world's largest swamp – in the Sudan. Political upheaval and the difficulty of any travel in a swamp have kept this place interesting for explorers.

6. Cave systems anywhere; for example the huge Voronya Cave in Abkhazia, Georgia, the world's deepest, which revealed more undiscovered passages earlier this year.

7. Mountains in the extreme east of Tibet. 159 out of 164 peaks over 6,000m are unclimbed here and mostly unnamed. Hard to get to but surrounded by huge unclimbed peaks and micro-areas of fertility in deep gorges. Shangri-La style, there could be more waiting to be found: in 2002, such a fertile oasis was found in the Himalayan reaches of the Tsangpo river.

8. Chukchi region of Siberia – the very far north-east of Russia. Due to economic collapse people still live in a traditional way herding reindeer and living in skin shelters. Apart from Roman Abramovich, that is, who bizarrely maintains a villa here – testament to his time as governor of the region.

9. Spice Islands, Indonesia. A huge number of small islands with rarely visited interiors between New Guinea and Sulawesi. Recently opened up after years of Muslim / Christian violence.

10. The myriad tiny feeder rivers and streams of England, Scotland, Wales and Ireland. Unlike footpaths they are very rarely travelled. Chances are there is one within a mile of your house. Buy some waders, or an old scout-group canoe and go exploring today.

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