ART BUCHWALD says he goes back to Martha's Vineyard every summer for two reasons: First, he owns a house A there, "so I have to go and see about my house." And second, the return visits give him a chance to see old friends and neighbors--like Lillian Hellman, William Styron and Mike Wallace--whom he doesn't see the rest of the year, "so they haven't heard my jokes yet."

Others go to the Vineyard for the sun and sand and socials, as well as the privacy that comes with being a small out-of-the-way island with steep prices.

But seven of us found a way to visit Martha's Vineyard last summer and sample the best of the sights and sounds of this celebrated triangle of sand--while keeping the cost to a minimum. We rented a four-bedroom house for one week, took turns cooking meals and spent our days sunning, clamming and biking. My expenses for one person for the week came to just over $700, including round-trip air fare from Washington to Martha's Vineyard, housing, food and expenses.

For the most part, we were all enchanted by the bright gingerbread houses, colorful seaside cliffs and small picturesque harbors of Martha's Vineyard. The weather, which is especially unpredictable on the island, was sunny and crisp enough for sweaters in the evening. And our group living experience worked out well, thanks toour compatibility.

Two friends, who had made arrangements to rent the house, were first to arrive on the Saturday our week began. They drove up from their home in Hartford, Conn., and ferried their car to the island so we would have transportation to get around the Vineyard, which contains 108 square miles of vastly different terrain, including forests, wild heaths dotted with lakes and ponds, and sandy beaches. Besides Edgartown, the best known and most commercial of the local towns, there are several major settlements, such as Vineyard Haven, Oak Bluffs and Menemsha.

When I arrived at the Vineyard airport on Saturday afternoon, my friends were there to pick me up. Two other couples drove from Hartford to Woods Hole, parked their cars and came over on the ferry on foot. We transported them, their baggage and their bicycles to the house.

By Sunday we had settled into the house, a gray, weathered structure with four bedrooms downstairs and a kitchen-dining-living area upstairs. Our address put us between Edgartown and Katama Beach--just the right distance for a bicycle ride.

We had paid $1,150 for the week--or $287.50 per couple. What we got was a fairly modern house set in a field near a dairy farm. The view on a clear day included black-and-white cows grazing nearby and a bit of the Atlantic Ocean on the horizon--if you knew where to look and stared hard. Our kitchen was well stocked with dishes and pots, and the bedrooms had pillows and blankets.

House rentals vary enormously in price, depending on location and size and condition of house. Many realty firms prefer to rent for the season, from June 15 to Sept. 15. Judy Stimel, president of Avery and Co., an Edgartown real estate firm, said her seasonal rentals range from $3,600 for a three-bedroom camp house in an out-of-the-way location to $40,000 for a luxury house in a prime setting.

Some weekly rentals also are available, but they are more difficult to get. To find out what is available, write for copies of the Vineyard Gazette, Box 66, Edgartown, Martha's Vineyard, Mass. 02539. Each copy is $2, and the classified section probably has the widest selection of housing.

During our week on the Vineyard, we explored as much of the island as we could, trying to balance our sunning time on the beach with other activities. Some memorable experiences:

* Riding the bicycle path from Edgartown to Oak Bluffs on a 20-mile round trip that provided views of the ocean, the beaches and the wildlife.

* Walking through Trinity Park, the old Methodist campground where a collection of 320 small gingerbread houses dating back to the late 1800s has been maintained and painted rainbow colors of pink, green, yellow and blue. The effect is reminiscent of a living museum of dollhouses.

* Attending the West Tisbury county fair, with its craft exhibits, fiddlers' contest and opportunities to stuff on tempura, fried doughboys and lemonade.

* Taking the two-hour ferry ride to Nantucket to spend the day walking the cobblestone streets, visiting the wooden saltbox house built in 1686, ogling the expensive baskets and handicrafts in the shops and peering out to sea from the tower of the Congregational Church.

* Riding the Flying Horses, built in 1876 in Oak Bluffs and thought to be the nation's oldest carousel. Listed in the National Register of Historic Places, the carousel still dispenses brass rings to riders spinning by on wooden horses.

The only sour notes came when we went to Martha's Restaurant for our one big night on the town. We had made reservations for a balcony table, but the management refused to seat us there. We were shuffled to a less desirable location and were kept waiting so long that some of our group were on the verge of starvation when food finally arrived more than an hour after being ordered.

In addition, I learned belatedly that the police operate a speed trap on the road to the Gay Head Cliffs, where tourists go in the evening to watch the sunset. Police also ticket cars parked on the shoulder of the road near the entrance to the cliffs.

The regulars who go to Martha's Vineyard have developed their own style of living over the years. And because the names of the regulars are so well-known, the island and the style have acquired a certain mystique. But Buchwald says that has given some people the wrong idea about what goes on on Martha's Vineyard.

"It's a perception of some people that Jackie Onassis and Walter Cronkite and Edward Bennett Williams and I all live in the same compound, go swimming in the same pool and then go in to have dinner in the same dining room," he said.

"The impression is that we're together all the time. But that's not the case. A whole summer can fly by and you won't see Jackie or Walter or Edward," he said.

However, Buchwald says, the Vineyard summers are simply great for families. "If you like the sea, you can go to the sea," he said. "If you like sailing, you sail. If you like to look for mussels or clams, you can do that."

Buchwald says he uses his time on the Vineyard to "read, make spaghetti, eat lobster, do a little work and entertain." The Buchwalds rarely travel more than five miles beyond where they live in Vineyard Haven, he says. "If you are asked to go to Chilmark (18 miles away) or Edgartown (10 miles away), it's like being asked to go to Tucson, Arizona, so we don't go usually," he says.

Instead, they stay close to their neighborhood, an area that could be called Writer's Row. "Mike Wallace has the first house, Lillian Hellman is there, then me and John Hershey and William Styron," Buchwald says.

"We have control of the row; we can throw out anyone whose books we don't like."