Facing down fears and scaling peaks in the Grand Tetons. At the famed Exum school, learning to climb is safe - and exhilarating

I'm feeling rather secure here on a five-foot rocky shelf halfway up this 150 -foot granite wall. The sun splays across the Grand Teton landscape, its jagged, snow-lined peaks above and endless brown plains below. Easing the belay rope around my waist, I watch as a fellow classmate scales the rock slope beneath my feet.

Suddenly, there are shouts from above: ''Pull the left hand to the bottom of the right. Don't let the brake hand go!'' I look up. Our climbing instructor is upset.

Tussling with the rope, I momentarily forget which hand is right and which is left. ''Slide the rope through the right hand. Never let the left hand go!'' Finally, seeing my mistake, I regain my confidence and do it right. The instructor comes down the wall and reinforces his directions. I won't make that mistake again.

This is Exum - the Exum Mountain Guide Service and School of American Mountaineering, considered to be one of the finest climbing schools in the country, and probably the world. And this is Exum's Basic School, a day-long introduction to the fundamentals of climbing, rappelling, ropes, and knots.

This particular morning there are two basic classes up climbing the training walls, including four women, a middle-aged man, and 15 young men. To the right of us are a young couple and their 12-year old daughter in an intermediate class. It is clear from the groups assembled that you don't have to be 21, male, and a little bit crazy to learn how to climb mountains.

The couple and their daughter are climbing ''The Open Book,'' a fearsome-looking 50-foot section of steep rock that is split open like two halves of a book. At this point, the feat looks almost unattainable, but by the end of the day most of our group will eagerly sign up for intermediate class and the climb.

With Exum's expert training, that's not an uncommon occurrence. Each summer, Exum brings in more than 20 of this country's top mountaineers to teach the young, old, and adventurous ''the ropes'' of climbing mountains. Today, our guide is Jim Bridwell, one of America's foremost rock climbers, a man whom Outside magazine recently called ''Ace of the Big Walls and Admiral of Yosemite.'' He has pioneered six routes up El Capitan and two on Half Dome. And he is helping lead an American expedition up Mt. Everest next spring. We are obviously in good hands.

He begins the day with a detailed lesson in ropes and knots. ''The rope is a creative animal,'' warns Bridwell, ''it will do things you don't expect it to do.'' He shows us the two basic knots of climbing, the bowline and figure-of-eight. ''Order is the prelude to sanity - and safety,'' says Bridwell.

The Basic School is meant to be an easy, nonstrenuous, and confidence-building introduction to the sport, and despite our anxiousness, our first ''climb'' is up a 10-foot gently sloping small boulder. Bridwell demonstrates the two types of foot holds: smearing, in which the foot is flat to the rock, and edging, where the boot is used to wedge into the rock. Fitting hands and feet into the small ripples of the rock begins to feel natural: and so on we go to the first real climb.

At the base of a 150-foot moderately sloping wall, Bridwell displays the climber's basic equipment, and how to belay - which literally translates ''to make fast'' - a person climbing up to you on rope. The lesson is quick but clear , and the climb starts.

On the first part, Heather, a girl from Oregon, gets stuck on a ledge. Bridwell shouts: ''Stand up. Get your weight away from the rock.'' Slowly, warily, she gets off her stomach and regains her confidence. The group cheers her on, and when she finishes, shouts of ''Good job'' and ''Way to go'' accompany her arrival.

More than anything else, rock climbing breeds brother-sisterhood. Trust and support are vital, and without them danger seems to increase exponentially.

During lunch Bridwell talks of his many experiences climbing: It is an added bonus to the day (although a probable one that any class will have, since many of the guides are world-class climbers).

''Be good to your rope; it will save your life,'' Bridwell advises. And then he tells of a 14-story fall (140 feet) he took. The rope, he says, saved his life.

On another climb last winter, he says he let pride get the best of him and went onto a hanging ice waterfall without ropes or his trailing companions. The result was a 100-foot fall: ''I fell 40 feet in the air, but turned myself around as I fell and landed on my feet.'' He slid down the ice another 60 feet. ''You learn how to fall correctly - although the point is not to fall - but most climbers do.''

Soon, it's back to the granite and on to rappelling. This is the thing that most scares novice climbers - most people have images of a person bouncing and sliding frighteningly fast down a 200-foot overhanging cliff. Well, that's not the way you start at Exum.

The Basic School rappel is down the same slab you just climbed - not more than a 70-degree angle - and no more than 40 feet. With the gentle slope and plenty of encouragement from fellow classmates, most of our group made it down easily.

Just then it started to rain, something that occurs frequently in the Tetons mid-to-late summer. While waiting out the storm under a ledge, Bridwell and I discussed something that he says professional climbers spend a lot of time thinking through: the dangers of climbing.

''To me, climbing is a spiritual half-way point,'' says Bridwell. He explains that falls of his own and friends' mishaps have forced him to discover deeper meanings in his climbing.

Sadly, Bridwell has also had several friends die on climbs. But despite his own falls, ''I know that I won't die until I've learned what I've needed to learn here.''

The day's schooling finishes with an overhanging rappel of about 50 feet. Here, we sense for the first time some of the more challenging aspects of climbing: At one point you have to leap out and down from the rock wall, descending for about 30 feet in the free air, spinning slowly about the rope. Despite apprehension at first, most of the group are enthralled with this challenge and go away with a feeling of exhilaration and accomplishment.

As we descend, it starts to drizzle once again, but no matter. Smiles and laughter punctuate the trail downward as Bridwell leads a fast scamper over small rocks and thick brush. When we arrive at the hut, there is a warmth and a shared inside feeling - a joy that, as climbers know, comes from facing down fears and scaling peaks. Practical information:

The Basic School costs $37, and you bring your own bag lunch. Following that, Intermediate School ($48) is recommended before going on a climb of any of the major peaks in the area. For those who go through the Basic and Intermediate Schools (and there are many novices who have done this), a two-day guided climb up the Grand Teton - one of the classic rock climbs in the world - starts at $ 140, everything included. I climbed Mt. Moran - one of the more difficult peaks in the region - and it was an unforgettable experience.

To reserve a place in a class or one of the climbs, you must write or phone at least one day in advance. Exum's summer address (June 11 to September 11): Box 56, Moose, Wyo. 83012; or call (307) 733-2297. The school's winter address: 2627 Lombard Street, San Francisco, Calif. 94123; or call toll free (800) 551- 1769.