One of the best ways to sightsee Down Under is to dive down under.

There are many ways to immerse yourself in the spectacular world of Australia's Great Barrier Reef. I had chosen to explore it on an all-day excursion aboard the 100-foot catamaran Quicksilver, which whisks up to 275 passengers to the outer edge of the reef, where they can snorkel, scuba dive or view the wonders of the depths in semi-submersible "submarines."My reef adventure began when a bus picked up a small group of tourists at the Kewarra Beach Resort outside Cairns (pronounced Cans), one of the major gateways to the reef on the coast of Queensland, Australia's "Sunshine State."

The 45-minute drive north to Port Douglas was spectacular, twisting between the sea and rain forest-covered mountains.

Promptly at 10 a.m. the Quicksilver pulled away from the dock and sped out to open water, trailing a white wake in the glassy blue sea.

Cruising at 27 knots, it arrived at its anchorage at Agincourt Reef 90 minutes later. During the 40-mile voyage, a marine biologist gave a talk and slide show, only partly allaying our fears about sharks: "They're only four to five feet long in these waters and shouldn't bother you."

Agincourt Reef lies at the edge of Australia's continental shelf, on the brink of a deep Coral Sea trench. It is just one of 2,500 individual reefs and 71 coral islands that make up the 1,250-mile Great Barrier Reef along the country's northeast coast.

The largest living structure on Earth, it is more than 10,000 years old and still growing, thanks to the unending work of millions of coral polyps, tiny limestone-secreting marine animals.

The reef - which has been protected since 1975 as the world's largest marine park - also is the home of 1,500 species of fish - from blue tang to black marlin, from moray eels to manta rays, from giant grouper to butterfly cod - and, of course, sharks. All thrive in the warm, clear waters with visibility of 50 to more than 150 feet.

We were eager to plunge in and see for ourselves.

A floating platform (permanently moored to Agincourt Reef) offers a sun deck, a ramp for swimmers and snorkelers to enter the water and an underwater observatory for dry viewing.

Another option - for those who want a diver's-eye-view but don't want to get wet - is to take the free 35-minute trip in the 28-passenger semi-submersible sub. With windows just below the waterline, it cruises at three to four knots over coral canyons teeming with marine life.

My choice, though, was scuba diving. I had earned a diving certification card just a month before in anticipation of my Australian trip.

Seven divers and the divemaster boarded a small tender that took us to the first dive site - Nursery Bommie (bommie is an Australian word for a coral pinnacle).

After donning the heavy scuba gear, we plunged into the crystal-clear water and were instantly weightless. Descending 60 feet, we reached the base of the bommie. It was surrounded by multicolored tropical fish of every type, shape and color. Some were bold and swam right up to our face masks, others darted away.

The divemaster pointed out a hovering barracuda; these fish have razor-sharp teeth but are not normally a threat to divers. There were new wonders as we spiraled upward, and those of us with underwater cameras recorded the adventure.

The second dive took us outside the reef, where we descended to 30 feet and let the current drift us in, passing over a maze of coral formations. It was here that we spotted a four-foot shark, which showed no interest in us at all.

The two 40-minute dives were over too quickly. The cost was $25, including all gear. This was in addition to the $59 tab for the all-day cruise on the Quicksilver, which included free snorkeling equipment and a smorgasbord lunch. Transportation from Cairns was $6.75.

Many other dive boats service the reef. Options include taking a mainland-based trip (as I did), booking a live-aboard voyage to some of the remote reef sites or staying at one of the island resorts.

There are only three islands directly on the reef itself - Heron Island, Green Island and Lady Elliot Island.

Among other well-known resort islands are Dunk, Bedarra, Hayman, Hamilton, Hinchinbrook and Lizard. Capt. James Cook named many of the islands during his exploration of the coast in 1770.

A new attraction - in effect a manmade island - is the 200-room floating hotel permanently moored at a lagoon on John Brewer Reef, 44 miles northeast of Townsville, another major gateway to the reef. The $40 million, seven-story Four Seasons Barrier Reef resort hotel offers such amenities as two dive boats, three restaurants, tennis courts, a health club and direct-dial phones to the outside world. It can be reached by helicopter, float plane or high-speed catamaran.

The floating hotel is only the latest new tourist facility along the Great Barrier Reef. Other new developments include the $200 million (Australian) remodeling of the luxury resort on Hayman Island, the 200-room Ramada Reef Resort north of Cairns and a "walk-through" reef aquarium in Townsville.

The boom in tourism is reflected in a 50 percent increase in international visitors to Queensland since 1979, and that's not including the massive impact of World Expo 88 (now through October) in Brisbane.

Besides diving, Great Barrier Reef attractions include sailing (especially in the Whitsunday Islands), bird-watching (especially on Heron Island) and black marlin fishing (especially around Lizard Island).

Year-round the Great Barrier Reef enjoys a tropical climate. Since Australia is south of the equator, the seasons are reversed. The most rain falls during their summer - January, February and March.

One of the best times to visit the reef is during their winter and spring. Over the year, water temperatures average 72 to 78 degrees.

For more information, write for the "Aussie Holiday Book," which is available free from the Australian Tourist Commission, Suite 2130, 150 N. Michigan Ave., Chicago, Ill. 60601.