Holland America's Nieuw Amsterdam takes you to Mexico in the highest of style

Steve, who works nights in a Hollywood film lab, is discovering the joys of table tennis on the Upper Promenade Deck. ''I never had time before,'' he says; ''it's that simple.''

Ken, an actor from New York, is jogging around the Promenade Deck. Lloyd, a Los Angeles doctor, is eight decks down, running some clothes through the self-service laundry, just to have fresh things for tomorrow in Ixtapa, our first port of call.

These were passengers, spread among the nine levels of Holland America's Nieuw Amsterdam, $150 million worth of French-built cruise ship, bound for Puerto Vallarta, Zihuatanejo/Ixtapa, and Acapulco in seven days, with the same time back to San Francisco.

This is, after all, the world's newest luxury liner - 10 decks from the Sun Deck, where volleyball, golf, and just strolling are perfect, down to D Deck, reserved for crew and storage. This seaworthy hotel is 704 feet long, with a staff of 580 (including 57 chefs), all to serve 1,210-plus passengers.

The Nieuw Amsterdam made her maiden transatlantic voyage July 10, after a technical problem delayed delivery. She won't be Holland America's newest ship for long, however; her sister ship, the Noordam, is scheduled to be delivered in April.

The new vessel incorporates the smartest in ship design. Even the stern was redesigned, squaring it to give more deck space and larger cabins.

The ship serves Alaska and Mexico from her home port, San Francisco. But the draw is not limited to the Bay Area. Holland America offers ''fly/cruise'' packages that include the price of air travel in your cruise ticket, arranging everything down to the baggage handling. As with its Caribbean, Bermuda, and Trans-Canal service on the Volendam, Veendam, and Rotterdam (out of Ft. Lauderdale and occasionally Los Angeles), it makes it easy to join the ship from wherever you live.

At embarkation, Capt. A. J. Hess turned away almost 2,000 bon voyage visitors. ''That's my only objection to the port facilities of San Francisco, really, that the wharf is just not adequate for crowds of 5,000 people, passengers, and guests,'' he says. After 32 years at sea (all of them with Holland America), he knows whereof he speaks.

We were to spend a week sailing south to Acapulco, where the divers still leap from the rocks for tourists, where Henry Kissinger spent his honeymoon, and the Shah of Iran bought - but never lived in - Merle Oberon's villa. A stop was scheduled at Puerta Vallarta (Mazatlan and Cabo San Lucas for those on the second, returning, week), with a day to explore the starkly contrasting world of poor Zihuatanejo and showcase Ixtapa, which is not a town at all, but a lineup of nine luxury hotels set on a spectacular powder-sand beach - set there in a row like so many children's building blocks by Mexican government fiat.

This seven-day southward sail, with flight home, is called the ''Seafarer''; join in Acapulco and sail to San Francisco and that is the ''Wayfarer.'' Each week is almost evenly divided: half the time at sea, half in ports. Just when you are passing from enjoying the peace and a certain monotony of sea life, onto land you go.

We had a full house aboard the 33,000-ton beauty as she sidled out of San Francisco's Pier 35, her navy-blue hull obscured by streamers and confetti. People had parties in their staterooms, the Indonesian cabin boys carried flowers and fruits, and the feeling was genuinely festive. The magic was there, with the elegance of the Rex, Fellini's luxury liner that cruises in and out of ''Amarcord,'' without the fascism.

Inside, Holland America has not tried to be cute, and the ''theme'' approach is nicely handled. The motif of Dutch Americana is carried through the public spaces with 17th-century maps, historical documents, and statuary recalling the period after 1626 when the Dutch West India Company purchased Manhattan Island for $24 worth of trinkets from the Canarsie Indians. ''The Square,'' amidships on Main Deck - which includes the Front Office for paying bills, buying stamps, and getting questions answered - really works as the floating village piazza the ship's designers intended. People stopped and talked, felt well oriented (a problem passengers cited on other ships), and gathered for dinner.

Even though this sailing of the Nieuw Amsterdam came after she had been through sea trials, an inaugural Atlantic crossing, and two previous other voyages, she showed no signs of wear whatever. It was impossible to walk 50 feet from your cabin without encountering a crew member polishing a window, vacuuming the carpets, polishing brass, and returning your smile.

In ''value season'' (Oct. 1-Dec. 17, 1983, and March 24-May 12, 1984), the median price for a double stateroom for seven days is $1,500 to $1,700 - depending on how far you fly to and from San Francisco.

In peak season (Dec. 24-31, 1983, and Jan. 28-March 17, 1984) you can expect to pay more: the price will be about $200 higher.

So the band played us over the gangplank and a cruise photographer snapped us as we boarded. The Dutch officers in crisp white uniforms greeted each passenger with ''welkom aan boord!'' The horn blasted, and without benefit of tugboats (the ship has the latest in auxiliary propellers for moving sideways to and from pierside), we embarked. It was punctual, just as would be every arrival and sailing, every ringing of the dinner chimes, every event without fail. You came to know that when the shore excursion director, Ron Miller, said ''tenders will ferry passengers between ship and shore from 9 a.m. to 11 p.m., about every 20 minutes,'' you could count on it.

Nightly shows in an impressively equipped nightclub-lounge (called the Stuyvesant) delivered something for almost every taste: a performer who does animal imitations, a precision dance team that offers free ballroom dancing lessons in the afternoon, a duo of tenors, a quartet of singer-dancers who perform everything from country-and-western to Broadway show tunes. There was plenty of dancing: disco on one deck (open until the last patron floated out) to a ballroom, where couples in formal attire (two nights out of seven) waltzed and did the foxtrot to musical chestnuts. I have never seen more people, many of them (but by no means all) of grandparenting age, have more fun.

Arriving in Zihuatanejo, we were ferried ashore to tour on waiting buses, or be left to loll the beaches, our comings and goings from shipboard monitored by attentive crew and cameras, watching to be sure passengers were loaded safely onto shore tenders.

The ''hotel'' staff is an autonomous division, and could run any five-star hostelry on land. Their spontaneous smiles for everyone could not be programmed or taught. And theirs is friendliness not paid for: Holland America observes a strict ''no tipping required'' policy. Passengers are told ''you should feel free to reward someone for exceptional service.''

The Nieuw Amsterdam produces 6,000 meals every 24 hours: breakfast, lunch, and dinner, with waiter service, which I found as first-class as the edibles. That includes mid-morning and mid-afternoon snacks and the midnight buffet - above the three giant daily meals out of a spotless kitchen (I checked).