PIRAEUS IS where it all begins. Piraeus shrieking with life at barely 8 o'clock in the morning, with your taxi stuck in harbor traffic while 100 yards away ships leave for everywhere. But somehow you make it okay, scrambling up the wobbly steps as the anchor comes up and the ship adds its note to the dockside cacophony. All the ships seem to be hooting now, all straining to sail at 8 a.m. Is it a contest? How can be a race when all the ships are heading for different places?

For those seeking a seagoing vacation, Greece is a particularly fortunate choice, most of its territory consisting of hundreds of islands connected by an elaborate network of ferries. Given the distances that must sometimes be traveled (Crete or Rhodes are at least 12 hours' voyage from Athens' port of Piraeus), almost every journey is a cruise in itself: a time to bask in the sun, to catch up on that long-neglected best seller or those overdue letters, to eat, drink or merely snooze.

In a manner of speaking, then, wherever you go in Greece you'll be taking a cruise of sorts; every ship between islands is an adventure guaranteeing at least an hour of complete lassitude in the scorching sun. And whether you prefer to pay extra for an air-conditioned lounge in which to relax, or keep the expenses down by sharing deck class with the backpackers is up to you, but cabins (usually available without prior reservations) are an unnecessary luxury in the daytime. At night it's worth the extra drachmas -- at least on long trips -- to stretch out, but you may well be happy under the starts -- in which case have the foresight to bring an air mattress and a blanket.

Domestic shipping varies a good deal in comfort and ambiance, but the boats operating between Greece and Italy are miniature floating resorts complete with restaurants, bars, shops, swimming pools, even discotheques. Shorter trips between adjoining islands are little more than elongated rides on the Staten Island ferry. Hydrofoils servicing the nearby Argo Saronic islands west of Athens, and onwards down the Peloponnese coast, attract the sea-loving traveler for whom speed is paramount. This includes an increasing number of Athenian commuters.

But if you travel in groups or yearn to steer a boat of your own, best of all are the yachts and motor boats of all sizes that are available for charter; by day or by week, with crew or without. With a chartered yacht (rates range from less than $100 per person daily), the choice of itinerary is yours, and it can take you as far off the beaten track as you wish.

Of course, one of the debatable charms of nosing into the tranquil harbors of islands rarely visited by tourists, is that such places sometimes lack all the usual amenities -- no restaurants, for example, which obliges visitors to acquire canned corned beef at the solitary store or possibly to negotiate with a fisherman for his newly landed catch. But this is a minor drawback compared to the delight of being moored in a harbor where the only voices are Greek and whose quayside kiosk is not plastered with garish London tabloids.

Anyway, a meal on deck supplemented perhaps by an inexpensive bottle of Greek wine and accompanied by the keening cries of seagulls waiting on the wing for leftovers can be one of nature's true delights. (The Greeks, incidentally, claim to have invented wine -- around 1500 B.C.; encyclopedias say the evidence is inconclusive.)

Collecting food for such alfresco picnics an be an adventure in itself, especially if the shopping takes place in the crowded but colorful market area along Athens' Athinas Street, where hanging sides of meat, open sacks of legumes and boxes, barrels and jars of just about everything edible are a reminder that not everybody buys their food processed and packaged. Tucked away amid this apparent chaos are the cluttered grocery stores that specialize in imported foodstuffs from around the world: canned beans, German cookies, Polish hams, French preserves, Dutch cheeses, English fruitcakes.

Most of the regular interisland ferries sport dining rooms serving bland meals at fixed times. Snack bars offer toasted cheese sandwiches (a tourist staple throughout Greece) plus typical international junk food of the potato chip genre. There are always coffee and sodas available as well as the sublimely icy glasses of water for which the country is famous. Yet the wise island-hopper comes prepared for an impromptu picnic at any time even though every day will produce a fresh harbor with its cafes and tavernas.

It is hard for the first-time visitor to comprehend just how varied Greek islands can be, not only geographically but in the distinctive ambiance that is sometimes too subtle for the overnight tripper to detect. Occasionally the difference is obvious; between, for example, lively Ios and sombre Patmos in one of whose grottoes St. John legendarily heard the voice of God through a crack in the ceiling. Such is the dominance over Patmos, even today, of the 11th-century Monastery of St. John Theologos, that the pint-sized island (15 and a half square miles) has virtually no night life -- and certainly no discotheques. Overcrowded Ios, on the other hand, a backpacker's paradise, sometimes seems to have nothing much else.

One thing almost all islands share, however, is an astonishing capacity for inducing a totally irrational possessiveness. This phenomenon -- remembered later with amazement by many a shamefaced traveler -- goes something like this. As the morning boat from Piraeus docks at, say, Hydra, the disembarking passengers thread their way along the cafe-lined quay under the amused and curiously hostile glances of many already relaxing over a late lunch. Stranger in a strange land indeed! The newcomer knows in his/her heart just how it feels to be the outsider at a party. Laughing and joking, table-hopping and drink-swapping, the bronzed, barely clad wunderkind in residence are clearly indifferent to -- or could it be? actually contemptuous of -- the helpless, homeless, bag-toting strangers.

But wait. Now it is 24 hours later and guess who is sitting at these very same cafe tables, exchanging light-hearted banter with neighbors and scornfully watching the new arrivals disembark? "Look at all these tourists, " the 24-hour veteran is saying. "Why do they have to keep crowding into my favorite island?" Day after day the scene repeats itself endlessly.

It still seems necessary to remind visitors that Greece, like most parts of Europe, is much more accessible earlier and later in the year than in the midsummer months when Mykonos, for one, has been known to ask shipping agents to embargo tickets for that island. In July and August rooms are at a premium on all islands, even the least-visited, some of which have only a handful of private rooms and possibly one hotel at most.

In addition to lower prices, another advantage of early visiting, especially really early, such as late April or the first weeks of May, is the relaxed friendliness of the waiter or cafe owner who has time to banter with his customers, to ask them if they know his cousin in Baltimore, New Jersey or Florida. (Every Greek waiter has a cousin in Baltimore, New Jersey or Florida. Another certitude is that every waiter on Corfu is named Spiro.)

The major shipping lines occasionally operate cruises on smaller boats, but usually concentrate on the high-priced market. Last year, for example, Saronic Cruises was offering saven-day excursions aboard the motor yacht Ioannis, whose dozen cabins accommodate a total of 35 passengers. This year the Ioannis is being operated on seven-day cruises around the Cyclades by long-established Viking Tours, a company with an exceptionally benign reputation for its warm hospitality and do-it-yourself philosophy. Viking claims to have carried 150,000 North American passengers during the past 25 years.

Viking's cruise passengers, an arbitrary group of strangers who meet for the first time at an eve-of-sailing, onboard cocktail party, spend one or two weeks together at quarters close enough to suggest that anything might happen. There is the stuff of drama here. But such is the tact and experience of the charming hostess and crew that there are rarely any ruffled feelings. Friendships are made, as they say, for life -- or at least one exchange of Christmas cards.

The company's own two boats -- the 85-foot Viking of Kos and the 107-foot Blue Viking, each with nine 2- or 4-bunk cabins -- operate mostly between Mykonos and the Dodecanese islands, making brief stopovers at the Turkish port of Kusadasi with a side trip to nearby Ephesus, site of one of the wonders of the ancient world, the Temple of Diana, which dates from at least 10 centuries before the birth of Christ. The temple itself was burned down in 356 B.C. but a Roman copy of the statue of Diana rests in the local museum. It is exquisite -- as awesome as the six square miles of excavated and reconstructed ruins nearby.

In addition to Mykonos, islands on Viking's seven-day itinerary include verdant Samos, birthplace of Pythagoras and a wine famous long before Lord Byron's approving testimonial; isolated, mountainous Ikaria, and four adjoining islands strung out along the Turkish coast: Patmos, Leros, the sponge-fishing center of Kalymnos and flower-filled Kos, whose own famous son, Hippocrates, first codified medical knowledge more than 2,300 years ago.

Viking's 14-day tour, conducted at a more leisurely pace, adds the islands of Kythnos, Tinos, Delos, Ios, Santorini, Amorgos and Astypalea to the itinerary. In all cases cruising takes place only in daylight, the boat usually mooring at a different harbor by early each evening for an overnight stay. Departure dates for the 14-day cruises, which cost $1,190 per person in two-berth cabins or $1,090 in three and four-berth cabins, are April 29, May 13, July 22, Sept. 23 and Oct. 14. Departures for the shorter cruises ($695 or $645 per person respectively) are Aug. 11 and 26, and Sept. 9.

The Ionian islands of northern Greece will be the target of only two Viking cruises this year (June 10 and July 29), the 14-day odysseys tracing the ancient route of Ulysses past Zakynthos, Kefallonia, Lefkas, Paxi, Corfu, Parga, Nydri and Ithaka, among other places. Beginning from Piraeus the comfortable Blue Viking first negotiates a course through the Corinth Canal, a narrow channel that, begun by the emperor Nero in 62 A.D. but not completed until late in the last century, cuts 200 miles off the otherwise inevitable journey around the Peloponnese. These 14-day "Ulyssees Cruises" cost $1,690 per person.

Rates on all cruises include transportation to and from Athens, onboard accommodation, daily breakfast and lunch, all taxes and port fees and the full-time services of an English-speaking cruise leader. There is ample free time at each port to spend as you wish and the option, for a nominal fee, of taking various tours of the main points of interest on each island. The atmosphere on board is free-and-easy with books, games, maps and guidebooks available, and drinks on a serve-yourself honor system.

Viking's main office is in Athens but reservations can be made at and brochures obtained from Do-As-You-Like Tours Inc., 230 Spruce St., Southport, Conn. 06490 or (203) 259-6030.

At least two other Athens travel agencies offered slightly similar, inexpensive cruises last year -- Dolphin (25 Nikodimou St., phone 332-4197) and Zeus (32 Amalias St., phone 323-3391) -- but have not yet made their 1983 schedules available.

The cheapest and fastest cruises -- although a "fast cruise" would appear to be an oxymoron -- are those offered by various lines visiting three islands in one day, the islands being the Saronic trio of Aegina, Poros and Hydra. None is far enough from Athens to avoid intense overcrowding, and Aegina, on which many of the capital's residents maintain summer homes, is a singularly unfortunate choice. The daily cruise boats disgorge passengers by the thousands on the eastern side of the island at the once-sleepy harbor of Aghia Marina, whose populace springs to life as if the curtain had just risen on the latest performance. Cafe tables are neatly realigned (the last group having just sailed out of sight, the next group due one hour ahead) and the predominantly German signs replaced in the souvenir shop windows.

When the cruise ships docks there is just time for passengers to make the (expensive) side trip to the meagre 4th-century ruins of the Temple of Aphaia, one mile from the port, and then everybody is replaced aboard and the ship heads onward for the next island, where pretty much the same scenario (without the ruins) is repeated.

In truth, the ships -- Epirotiki Lines' Hermes and Saronic Cruises' Saronic Star -- are comfortably air conditioned with space for sunning, as well as bars and lounges; the Hermes' discotheque is matched by the Star's swimming pool. Each follows the same route at slightly different times, sailing early each morning from Piraeus' Marina Flisvos, and bookings can be made at the companies' offices in Piraeus, Athens or through any travel agency, as late as the night before sailing. Price for the one-day cruise, about $30, includes an indifferent but adequate lunch and is probably a bargain for tourists who want to see more than one island but have limited time. Saronic also operates one-day cruises to Mykonos.

Boats for hire begin with small sailboats (about 26 to 47 feet) from about $80 to $500 daily, with a skipper or crewman available for an extra $50. This category is known as "Bareboat." Next come motorboats and sailboats with auxiliary power (from 44 to 125 feet); capable of housing six to 10 people and complete with crew, they begin at about $550 daily. These rates are exclusive of fuel (which, of course, depends on the distanced traveled) or food, but these items, along with such accessories as windsurfing equipment and water skis can be arranged for an extra fee.

Most of the companies renting boats are located along the Piraeus waterfront, and many are members of the Hellenic Yacht Owners Association, whose richly illustrated booklet is available from offices of the Greek National Tourist Organization. Some of the bigger rental firms, such as Valef (for information in the United States, phone 215-641-1624), Eastern Mediterranean Yachting Ltd. (Marina Microlimano, Piraeus) or B. Koutsoukellis (3 Stadium St., Athens) produce pictorial brochures of their own. One of the most explicit listings is that of Seahorse (Marina 4, Box 10, Glyfada, Athens), whose brochure includes details of its U.S. affiliate, Swan Charter (Box 1447, Marco Island, Fla. 33937 or 813-394-5541).

Other yacht charters with U.S. addresses are the Greek Private Sailing Club (600 St. Andrews Rd., Philadelphia, Pa. 19118); Eagle Yacht Charters (150 Main St., Port Washington, N.Y. 11050) and Regatta Yachts (123 East 54th St., New York N.Y. 10022). Getting There

Scheduling: There is at least one daily departure, usually around 8 a.m., from Piraeus to each major island, less frequent service to smaller islands. Additional ferries to some Cyclades islands (Mykonos, etc.) depart daily from Refina, a small port east of Athens on the Attica coast.

Schedules vary slightly from season to season, are distributed free by the Greek National Tourist office in Syntagma Square and are sometimes available from GNTO offices in this country. Complete schedules along with fares, hotel rates, bus timetables and a wealth of other valuable information are listed in the monthly Key Travel Guide (about $5 from 6 Kriezotou St., Athens 134).

Interisland services: All islands are not reachable from all other islands; indeed it is often necessary to return to Piraeus from some distant point and begin again, or else make lengthy, out-of-the-way detours. After Piraeus and Rafina, the widest selection of interisland services are from Mykonos and Syros.

Access to islands of the northern Aegean is best made from Kimi on Evia's eastern coast, or from Ag. Konstantinos on the Evian Gulf; also from such northern ports as Volos and Thessaloniki. Most difficult to reach via Piraeus are the Ionian islands (Corfu, etc.) to which one proceeds more readily from Patras on the northwest Peloponnese coast.

Hydrofoils (Flying Dolphins) operate almost hourly from Piraeus' Marina Zea to the Argo Saronic islands of Aegina, Poros, Hydra and Spetses, thence down the Peloponnese coast to Monemvasia and -- when the seas are calm enough -- to the island of Kythira. Rough seas often cause long waits for service to resume and, in fact, it was interrupted so frequently on the Cyclades route last year that hydrofoils will not be usedin 1983.

Ceres, the company that runs the Russian-built hydrofoils, has 15 boats currently operating, each with a maximum 12-hour range without refueling and capable of achieving 32 knots per hour, about twice the speed of regular ferry boats.