The letter from Italy arrived one day early in June. Incredibly, a home exchange had come through.

Our family, Rachel, 13, David, 11, my husband Arnold and I, would be spending about four weeks in a three-bedroom apartment in Rome, with a villa on the Adriatic Sea at our disposal. Our correspondent, a doctor and his family, would spend the same time at our home in Washington.

Long, leisurely European vacations may be beyond the means of most Americans in the future. One way to ease the financial strain of travel is to exchange homes. But saving money is only the most obvious advantage of a home exchange. By stepping into another family's home, one can start out with immediate contacts in the community, a chance to experience the life style of the exchange family.

If the exchange families have children, the advantages are multiplied. Having a home base gives children a sense of security not to be found in hotel rooms. Strange foreign foods can be supplemented with familiar ones back at the house or apartment. The savings can add up on breakfasts, lunches, and even dinners prepared at "home."

There is a neighborhood to play in and to explore, with helpful neighbors to meet.

What does it take to find a compatible exchange? Comparing an earlier effort (that failed) with this successful one, I have learned a few things:

(1) Give yourself as many options as possible.

Our first form letter was sent to 50 people in 8 countries. There are several organizations that offer possible home exchanges. For a membership fee starting at $18, your name, and a brief description of your house, location, and travel interests are published in a directory sent to all members. From there, it's up to individuals to write and make their own arrangements.

We chose the Vacation Exchange Club because it has the most listings. At least one organization, Inquiline, will do a further screening of prospective exchanges, but the fee is higher.

(2) Be flexible in your choice of places.

There were relatively few listings in sought-after countries such as France and Italy. The greatest number of European listings were in England and Germany. Incidentally, it was almost worth joining to get the wonderful letters of rejection from the British, many of whom took the time to write a charming, personal note.

(3) Remember that it takes an investment of time.

For every interested response we received from our original letter, I wrote a long, detailed second letter tailored to the particular interests of the family involved. To our doctor in Rome I offered contacts with specialists in his field and friends in the neighborhood for his teen-age daughter to meet. i

The process takes months to complete. The first directory was published at the end of February, with a supplement in April.

(4) Be creative in promoting your own home and location to others.

Put yourself in the place of people coming from very different environments, and try to imagine how they would react to your area. Activities that your family takes for granted may be fresh and new experiences to others. Our own urban location is ideal for touring the many sights in downtown Washington, but I also stressed recreational facilities available and trips out of the city.

(5) Be realistic.

Europeans are sophisticated about travel in the United States, and they want to go to the best resorts and major tourists sites. That we found an Italian who wanted to come to Washington, D.C., in August was pure luck. It is not unique, however; we have heard of similar exchanges, some from people we wrote to who had already arranged an exchange here.

Far more likely is the prospect of exchanging within this country. One inquiry from a family in a scenic area of Colorado has given me an idea to work on for next year: a chance to see the West as reasonable cost for a family that has never gotten into camping. Other possibilities include short-term exchanges closer to home a week or a weekend in a big city for one in the country.

Once you join, most organizations leave all the responsibility to individual parties. There are no guarantees on the care of your house other than what you can work out with the other family. With careful planning, the risks can be minimized, and the rewards of exchanging are so appealing that the prospect seems worth the chance.

Our exchange will include the use of cars, yet another benefit/risk. As we fill our spare time these days reading travel books, road maps and Italian grammar, we marvel at the prospect of a vacation we never could have afforded any other way.