GETTING THERE: Sicily has two airports, one at Palermo and one at Catania. Flights from Washington can be arranged through Alitalia, Pan Am or TWA; the current round-trip Apex fares range from $759 to $889, with varying restrictions.

There are overnight train connections from Rome direct to Taormina, Palermo, Catania, Enna and Syracuse, and car ferries from Naples to Palermo and from Reggio di Calabria, the tip of the Italian boot, to Messina or Catania.

GETTING AROUND: At 175 miles long and more than 100 miles wide at its widest point, Sicily is the largest island in the Mediterranean. Though there are intercity buses and a somewhat leisurely train system, a car is a great timesaver and gives you flexibility in roaming from site to site. Generally we have found American car rental firms much more reliable and responsible than the cheaper local ones. Our inconspicuous Fiat cost about $150 a week.

The Sicilian autostradas are most efficient and can get you across the island in a few hours. The minute you get off these superhighways, however, and onto the ancient twisting country roads, you can forget about your schedule.

There is also a variety of package tours by bus that can be arranged in advance or in bus company offices in most Sicilian cities.

WHERE TO STAY: Though hotel rooms are available in most Sicilian cities even in the summer, it is worth writing ahead to be sure of accommodation at the smaller and popular places like the Villa Athena in Agrigento or the Belvedere in Taormina. Pleasant pensione rooms with view and garden are often available without reservations. Hotel rooms cost up to $50 a night double, pensiones about half that.

If price is no object and you don't mind being surrounded by rich Americans, try the San Domenico Palace, in a lovely sprawling garden surrounding an old monastery at Taormina. If possible, avoid the Jolly hotels, a Sicilian chain whose hotels are charmless and, we were told, overpriced.

WHERE TO EAT: Restaurants are everywhere, and we never bothered with reservations. For drinks, desserts and plain rubbernecking, the sidewalk cafe's are a delight. A trattoria dinner for two without wine runs around $15 to $20.

TIP: Stick to major traveler's checks. Every bank seems to have its own system for cashing checks, and in smaller towns you may have to go through several tellers to get action.

INFORMATION: Italian State Tourist Office, 630 Fifth Ave., New York, N.Y. 10020, (212) 245-4822.