As you motor up to it in a launch, Venice looks like a collection of those towers you make on the beach by dribbling sand and water. The skyline is such a delicate fringe of spires, steeples, towers, and pointy palazzo facades, that it's hard to believe some of it is 1,500 years old. Civilized Italians fled to the marshy islands off the east coast from Attila's armies, and by the year 421, they had started the city. Throughout a 1,000-year period of naval supremacy, they built up and elaborated on the little island as they built up their domain through trading and war.

Those gorgeous buildings are studded with the booty of Venetians' ventures. They're encrusted with early souvenirs. No wonder tourists' hearts lift as they arrive by train, boat, or car at the edge of this chimerical citadel. It was settled by people like themselves; more ferocious, perhaps, and more acquisitive , but sharing the same desire to go forth and see marvels and somehow to capture them.

From the water, Venice looks old, but too fancy to be venerable. You can't really believe it could have perched in such a decorative position for all these years. It's so low in the Adriatic: The water laps right up to the ornate curbings and marble steps of the palazzi, houses, and churches sloshing in the wake of launches, vaporetti (ferry-buses), and gondolas, and you can't really imagine a foundation of any sort down there.

It seems to be a free-floating fantasy, especially if you approach it by motorboat, as I did. Bridges with Gothic arches curve delicately overhead as your boat weaves its way along the canals and rios (smaller canals); you can glance down little streets and see cats, people, baskets, boots, and fireboats, all looking rather festive.

Step aboard the city, and it seems more solid. Not more ordinary, perhaps because the place is swarming with tourists and there is delight in the air. But it does stop seeming to bob on the waves, and you can see that the lacy walls of the Doges' Palace and the glut of decorative columns, colored marble, golden Old Testament scenes, and globular domes of Saint Mark's Church actually exist.

Venice has stopped sinking. But due to air pollution and high tides that sweep over St. Mark's Place so often that the Danieli Hotel keeps stands to put the lobby furniture up a little higher, it is still in an imperiled state. Close up, the great chunks of history are so stunning you forget to wonder whether it's real or not, or whether it will last, and just marvel that it's there and so are you.

Venice is a wonderful city to walk in, since there are no cars and the public transportation is by vaporetti in the canals. It is not, however, a place for getting from point A to point B. The streets go every which way, and the rios snake through, making their own distinct patterns. The Grand Canal is no help; it twists through the city in a backward ''S,'' so keeping track of it doesn't really tell you where you are.

They say the way to see Venice is to get lost, but in Venice you're never really lost. You don't exactly get where you were going, but is it a wrong turn if it takes you to a beautiful piazza complete with a tawny old church, cafes, and shuttered windows - or over a tiny bridge that lets you see over a 600 -year-old stone wall into a back garden with shaggy grass and lawn chairs? Of course not.

But if you prefer planned marvels to serendipity, there are signs leading to the major museums and sights posted just at the crucial nooks and crannies, leading you out the right end of squares that are never square.

If you'd like to ground yourself in Venetian art and see one of the nicer corners of the city, go to the Gallerie dell' Accademia.

The museum is also a good guide to Venice, since Venetian painters were no less struck by her beauty than the tourists, and you'll see the city pop up everywhere. One delightful painting by Bonifazio de Pitati shows God and a gang of cherubs sweeping over the city like a big wind.

Carpaccio painted the pageants and gondoliers and sea battles of Venice's literally splashy history as a merchant city and naval power. The detail is almost excruciating. Every gondolier paddle and bit of gold leaf is there, and there are many of both.

Giovanni Bellini's beautiful paintings of the Virgin show glowingly why Venetian painters are praised for their sense of color.

The mysterious ''The Tempest'' by Giorgione, shows a family on the grass with a city in the background and a flash of lightning breaking out of black clouds. The painting is so full of fine details, like the lightning and the leaves of a tree silhouetted against the mother's thigh, that it invites one to search for clues. It has been seen as Adam, Eve, and the infant Cain and Mary, Joseph, and the infant Jesus; but the current theory is that it refers to a popular romance of Giorgione's time and that the mother and child are Venus and Cupid.

Venice's churches are marvels. They surprise you by holding big bubbles of space under their domes and steeples that you couldn't imagine from the narrow stone walls outside.

Venetian architects knew about making the most of space. Go in Santa Maria Gloriosa dei Frari, built from 1250 to 1443. The lofty walls are pink brick that look as soft as faded corduroy, with old wood beams crossing the vaults of the ceiling in midair. Even on a rainy day, pearly light falls from way up top, illuminating a rich art collection that was spread out enough to enjoy.

Santa Maria della Salute is a big octagon, and Palladio's San Giorgio Maggiore, on the island of San Giorgio across the canal from St. Mark's place, is an exquisite cross-shaped building. Inside, the simple, symmetrical proportions and gray walls are soothing after a long day of sightseeing. This is a nice place to head out to at around sunset; then you can look west at Venice as the water starts to gleam and the domes change color.

Many Italian churches (and just about everything else but the restaurants) close from around noon until 2 p.m. Museums, such as the Accademia, close at two.

The Rialto Bridge is an old marketplace and was where the first of Venice was built. The fish market is under a row of Gothic arches in brick, and there are little stalls selling souvenirs, glass, and gloves in the narrow streets all around.

Venice, like all of Italy, is a great place to eat. Trattoria da Ignazio, which is near Campo San Polo on Calle Saoneri, has great vegetable soup, and the proprietor urged artichoke hearts and asparagus on me, which came artfully laid out on a long plate, the artichokes leafless and fried. This came to about 5,000 lire, or about $3.50.

The political side of Venice should be seen, not only to understand what paid for all the art, but because Venetian politics itself was an art. This city-state once negotiated separate peace treaties with all of Europe. The facade of the Doges' Palace looks like woven stone, with a band of pillars in the middle like lace, and what went on behind those walls was just as intricate and Gothic. It was here that the aristocracy got together and chose the doge, Venice's leader.

As the years went on, and the aristocrats pruned his privileges, the palace was a gilded prison for him. There was a regular stone prison down in the basement. The infamous, early secret-police group known as The Ten tried anyone they wanted to here. The Bridge of Sighs, which leads from more cells to the courtroom, is so named because the condemned got their last view of Venice from it and sighed. There is also a stone lion in one wall; informers used to push the names of those they accused of treason through the lion's mouth.

The walls are covered with paintings by Veronese, Tiepolo, and Tintoretto. Rather than postcard views, these are allegorical, with Venice appearing as a large beautiful blonde who is a close personal friend of Neptune. Go when it's light outside, as the paintings are hard to see. There is no electric lighting in the palace, and what the guide tells you is scary enough in broad daylight.

Saint Mark's Square, with its crowds of pigeons and tourists sunning themselves at the fancy cafes, is one of those huge expanses of city space that don't seem large. Crowded or empty, it's a good place to be.

The cafes are like fussy little chocolate boxes. A couple of them are lined in 18th-century murals. The windows are kept exquisitely clean, and the people sitting at their tables in front of such resplendent backgrounds look like paintings themselves. Two cups of hot chocolate one rainy afternoon at Grandcaffe Quadri cost about $7, but we sat listening to a string quartet, surrounded by lemon-yellow and gilt walls covered with little tableaux. It was a bargain, including as it did the Byzantine glitter of St. Mark's and the woven marble facade of the Doges' Palace.

Every hour, two lifesize statues of Moors gong an 18th-century clock. The four horses of St. Mark's, replicas of the real ones made in Greece about three centuries before Christ, survey it all from their perch with authentic enough hauteur.

The marble that covers St. Mark's as well as the Doges' Palace was imported, as were the paving stones of the square. The horses of Saint Mark's are spoils of the crusades. Venice is a city founded by refugees who, when they gained strength, became supreme tourists, a fact that makes the swarms of 1980s pilgrims, crusaders, and pleasure-seekers, following guides who quack all the modern languages, seem more at home here than anywhere else.

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