THE FISH HANGS vertically in the water, its green flanks and crimson-edged tail quivering slowly. A minT nowlike sharknose goby, normally a bite-sized morsel to the huge green triggerfish, swims into its mesmerized host's mouth to pick its teeth clean. After fastidiously checking every tooth, the goby emerges through the flaring gill openings, examines the luminescent scales on the triggerfish's body and descends to the coral head whence it came. The triggerfish shudders perceptibly and swims off. Behind, like customers waiting in a barbershop, are three or four other fishes, all in uncharacteristic poses, head up, head down, mouth yawning, signaling the goby, now perched on a brain coral, that their intentions are friendly.

This extraordinary symbiotic interaction at a cleaning station is being observed from a discreet distance by Margie and George Watt, retired and in their 60's, and their 14-year-old grandson Joey. Relaxed and floating at the surface of a warm sea, they watch the whole scene with fascination. The fishes, who seem oblivious to these ungainly creatures peering at them through glass-fronted masks, are only 10 feet from the three observers. Margie turns the plastic pages of a fish identification book searching for pictures of the "customers" at the cleaning station.

These people are fish-watchers, aquatic counterparts of bird-watchers. The water seems as clear as air, with huge tree-like elkhorn coral colonies visible 100 feet away.

Thousands of people have discovered that you don't have to be a macho scuba diver to enjoy this most accessible adventure. You may never climb Mount Everest, or trek across the Sahara, but you can afford the cost and you have the strength for a snorkeling adventure in the Caribbean.

Looking at the riotous colors of the reef and swimming among its inhabitants is to view one of nature's miracles. It will take your breath away. You may come upon a school of minnows or small herrings. As you approach the school, which may be 100 yards long and 10 feet high, a tunnel will form around you and the flashing silver fishes will be everywhere, like a rain of coins. The world turns silver and the tunnel seems to stretch to infinity.

If you can swim you can snorkel. In half an hour you will learn to breath through the J-shaped snorkel tube. People who feel insecure in the water often discover a new sense of security and freedom when they find they can breathe with their faces underwater. You stay at the surface, slowly swimming above the reef, careful not to disturb its inhabitants. Nowhere else can one view the denizens of a biological community so clearly. In a forest, the trees hide the animals; in a desert, there are few animals to see. But the coral reef is one of the richest communities, and it all hangs out for everyone to see.

How does one begin?

Try your local scuba shop first. It will outfit you with mask, fins and snorkel for $50 or $60. Buy a simple J-shaped snorkel, without pleats, a pinocchio-style mask without purge valve and full-foot fins (not rocket-style unless you want to splurge on scuba booties). Remember to wear thick gym socks with your fins, to prevent chafing.

The scuba shop may run trips to Caribbean and Florida resorts. Since you will not need tanks of compressed air, etc., you should pay the nondiver cost, usually about $200 less than the advertised fee. The dive shop may offer courses in a nearby pool. Their instructors will teach you how to snorkel in a few sessions. But you don't need the instructional services of the shop; you can do it all once you arrive at the resort. In fact, if you prefer, you may also rent the simple equipment at your hotel (not recommended, though, since they may not have a face mask that fits, and masks need to be properly fitted).

The key is to study ahead of time. Just as you rely on your Michelin or Frommer guidebooks when you visit Paris or London, so should you rely on your Peterson Field Guides when you visit a coral reef. Houghton Mifflin has published two such books in its Peterson series: one on seashells and one on coral reefs of the Caribbean and Florida. There are also the plastic books, sold in most dive shops, for identifying fishes underwater.

Almost every island in the Caribbean has fringing reefs starting right from shore, and bank/barrier reefs less than a mile out, the rear zone of which rises to a reef crest at the surface.

Bear in mind that the scuba diver, with all his paraphernalia and costume, sees little that you cannot see within 10 feet of the surface. It may be years before you become so familiar with the upper water phenomena that you will regret not seeing the various organisms that occupy the lower depths. To locate the best snorkeling spots, seek out a scuba operation at your hotel or nearby, and tell the divemaster you want to snorkel. He will be glad to take you to a shallow reef (for a fee) or direct you down the beach to a spot where you can swim right out to a fringing reef.

Some islands offer unusually good snorkeling. There are two sets of paired sister-islands that are bargains: Trinidad-Tobago and Curacao-Bonaire. In both cases, if you specify ahead to your travel agent that you want both islands, you can visit two for the price of one.

Tell the agent you want to stay on Trinidad (the other half of that exotic nation, Trinidad-Tobago). Many snorkelers enjoy the unusual experience of staying at the Monastery of Mount Saint Benedict, high on a mountain overlooking the beautiful campus of the University of West Indies. You can stay in its spartan guest house overnight. Through your open windows at night you may hear the steel bands, off in the distance, practicing for Carnival and their orgiastic moment in the sun.

The next day go to Carni Swamp to see the egret trees. At dusk thousands of white cattle egrets return to two or three trees in the center of the swamp, roosting in such numbers as to make the trees appear like giant snowballs. And then, a glint of red appears in the sea of white cackling and quarreling egrets. Unbelievably, other thousands of bright red, goose-size birds appear. The scarlet ibis are roosting in neighboring trees. It is a sight of such magnitude and color that you will never forget it.

But since Trinidad has virtually no snorkeling--it is so near the coast of Central America that fresh water runoff from the continent kills the coral--you may want to take off for Tobago, a 45-minute ride away. Tobago is a beautiful, jungle-covered island resembling Tahiti. Green mountains plunge into the sea; and there are only four or five hotels on the entire island. Buccoo Reef is at the western end and daily boat trips cater to snorkelers. The Crown Reef Hotel has a huge number of fishes right off its beach. Good snorkeling reefs are but a short boat ride offshore. Dive Tobago in Scarborough offers gear and lessons.

Another lovely pair of islands is Curacao-Bonaire. You can visit Curacao, which offers good snorkeling, without additional air fare. Besides, you will want to visit its picturesque old Dutch city, Willemstad, sample its tasty rijsttafel, and visit the oldest synagogue in the western hemisphere. Then take off for Bonaire, perhaps the best place for snorkeling in the Caribbean. Bonaire is a desert island--and take the word "desert" literally. Much of the island is covered with cacti. Because it rarely rains and there is no runoff, coral flourishes in the clear, silt-free water.

There is a flat, shallow platform about 50 feet wide surrounding the entire island. On it, many species of coral grow. Masses of elkhorn coral are interspersed with staghorn, brain, boulder and other corals. Fishes are large and tame. Some have been trained to poke into your pockets for bread. Clouds of yellowtail snappers, each a foot long, follow you wherever you go. You can snorkel off the shore anywhere.

All four major hotels on the island are, first and foremost, diving resorts. Aquahabitat is less expensive than the others and it is run by an interesting character, Captain Don, who is dean of diving in that area. The Flamingo Beach and Hotel Bonaire complete the price range, from moderate to expensive (Hotel Bonaire has a casino).

Another fine snorkeling island is Virgin Gorda, in the British Virgin Islands. There are fringing reefs almost everywhere, and several rather posh hotels from which to choose (cottages are less expensive). If you can afford the ultimate, Little Dix Bay Hotel, ask them to take you to the coral gardens off Mosquito Island. There, in water no more than a few feet deep, I encountered a school of man-sized tarpon, gliding like silver ghosts around a school of herring and me. There, one can literally walk to a flourishing coral reef.

Other famous snorkeling places are John Pennekamp State Park on Key Largo, Fla., the only underwater national park in the continental United States; and Buck Island and Trunk Bay national parks on St. Croix and St. John (American Virgin Islands) respectively. Boats sail to the reefs, catering especially to snorkelers, at Pennekamp and Buck Island.

Although little equipment is required, snorkelers should be constantly aware that they are in a foreign environment and must take precautions. It is desirable to purchase a B.C. (bouyancy compensator), and an inflatable life vest. In the unlikely event that you are caught in an offshore current and are swept out to sea, you will feel more confident if you can pull a cord and have your B.C. inflate, allowing you to float indefinitely until your buddy rescues you.

The dangers of snorkeling are primarily small ones--scratches and stings. Scratches may take longer to heal when constantly immersed in salt water. Jellyfish and sponge stings, unless one is especially susceptible, are about as painful as a bee sting, and disappear within an hour. But it is easy to avoid harm by dressing in a cotton long-sleeved turtleneck and light cotton slacks or leotards that will protect you from stings and scratches.

The most incapacitating of all threats is sunburn. When you snorkel, your face and half your body are under water, but the back of your neck and the tender skin behind your knees are exposed to the vertical rays of the tropical sun. Pull up your turtleneck and beware! Sunburn on the first day can ruin vacations.

If you are dressed properly, you won't be stung by a jellyfish or scratched by fire coral that sometimes surrounds an island. Fire coral looks innocent enough--like thin tan verticle plates with white tops. But the tiny animals that build the rocklike skeleton are hiding inside pinholes in the skeleton. When you touch them they eject microscopic poison darts (nematocysts) into your skin. These cause a painful red welt that soon disappears. It is easy to avoid fire coral by walking along the beach until you see a natural channel through it. Just line up the channel with a feature on the shore, a tree for example, and then carefully follow the channel until you swim past the fire coral zone. On your way back in, look for your landmark and you will find the channel.

The scariest animal on the reef is not the shark (virtually never seen inshore and behind the bank/barrier reef) or barracuda, which is absolutely harmless, but the lowly long-spined black sea urchin. It looks like a giant black pincushion with many 6-inch long black spines tipped with poison. But these urchins usually move less than a foot an hour and can't release their spines. Don't touch or step on one, and you'll be safe. They are common and if you brush up against one accidentally be prepared for the proverbial bee sting pain that will normally last not much more than half an hour. The tips of the spines will be visible under your skin as black dots. They will be absorbed and disappear within three days.

Some snorkel for relaxation, drifting almost motionless in the clear water, suspended between a white powdery beach fringed with palm trees and a reef full of brightly colored fishes. Others delve more deeply, seeking to understand the biological mysteries of the reef. Still others find snorkeling an esthetic experience--the waters of the Caribbean teem with innumerable masterpieces of nature's art.

In my experience, once initiated, no one has ever snorkeled only once.