AMERICAN travelers who know the value of a good bargain are heading for Europe this summer, taking advantage of cut-rate airfares and the new strength of the dollar against foreign currencies. But the savings don't stop there.

If you plan to shop in Europe (or elsewhere abroad), you should be aware that foreigners are exempt from the value-added tax that can amount to a hefty 20 percent or more on items you buy. But you must ask for the exemption, and the purchases must be shipped or carried back home.

Why pay more if you don't have to?

Customs procedures differ, and they tend to be bureaucratic, but the savings can be substantial. In some cases, the amount of your purchase may have to be above a specific amount, such as $50, to entitle you to a refund.

Generally, you can avoid the tax by having the shop ship your purchase home. If that is not practical (you're afraid the item may never show up), you must pay the tax but can apply for a refund. Ask the clerk for a value-added tax form, fill it out and present it to a customs official when you are departing the country. Possibly you may have to mail the form to the retailer yourself after a customs official has stamped it.

You can get the refund immediately at some airports that have special tax desks. If you have paid by credit card, the refund may show up as a credit on a future bill. Otherwise, the payment will be mailed to you, probably by check in the currency of the country you have visited.

The check can be cashed for U.S. currency at a bank or foreign currency dealer, though there may be a delay and a service charge. One dealer, Deak-Perera, promises to honor immediately foreign-currency checks with a U.S. value of less than $100. The fee is $3. Over $100, there may be a wait of several weeks while Deak-Perera collects from abroad. MAYBE NEXT YEAR: If you couldn't make Greece this year, the National Tourist Office of Greece sends along heartening news. By agreement of the organization of Greek hoteliers, the price for a hotel room in 1984 will be the same as in 1983.

For more information: Greek National Tourist Organization, 645 Fifth Ave., New York City, N.Y. 10022; (212) 421-5777. AFRICAN ODYSSEY: First, it's very expensive; and, second, it's a full year away. But for travelers interested in seeing new ports, the M.S. Lindblad Explorer is scheduled to make a 21-day cruise along much of the western seaboard of Africa, north from Matadi, the port of Zaire on the Congo River, to Dakar, the capital of Senegal.

Other stops include Libreville, Gabon (for a tour of the hospital built by Dr. Albert Schweitzer); Douala, Cameroon (to visit a tropical forest); Bioko, Equatorial Guinea; Lome, Togo; Abidjan, Ivory Coast, and Freetown, Sierra Leone. Sailing date is July 19, 1984; the ship carries 92 passengers, and the fare begins at $7,900 per person, not including airfare to Matadi.

For more information: Salen Lindblad Cruising Inc., 133 East 55th St., New York City, N.Y. 10022; (800) 223-5688. A CRUISE OF ANOTHER SORT: A swamp may not sound like the most attractive of places to visit, but there is a quiet loveliness in the forests of tupelo gum and cypress draped with Spanish moss found in the Great Dismal Swamp on the eastern border of Virginia and North Carolina, about an hour south of Norfolk.

For $1 an hour, travelers passing through the area can rent a canoe at Merchants Millpond State Park, just off U.S. 158 a few miles north of Gatesville, N.C., and explore a wildlife sanctuary and garden little changed in the years since George Washington visited the area.

Water lilies float on the 700-acre millpond, and occasionally wild swans or an otter can be seen gliding by. There are hiking trails, and primitive drive-in, canoe and backpacking campsites are available. Reservations are necessary for camping and canoeing.

For more information: Merchants Millpond State Park, P.O. Box 147, Gatesville, N.C. 27938; (919) 357-1191.

WINDSURFING HOLIDAY: One of the fastest growing participatory sports today is windsurfing, and the place to see how the experts do it will be in the Barbados this fall. The Caribbean island is the site of the 1983 Windsurfing Championships, scheduled from Nov. 20 to Dec. 3.

Islanders claim the stretch of beach from South Point Lighthouse to St. Lawrence Bay on Maxwell Coast, where the events will be held, offers superb sailing. The Barbados Windsurfing Club, providing instruction, rentals, pro-shop and repair facilities, was recently opened at the former Benson Beach Hotel on Maxwell Coast.

For more information: Barbados Board of Tourism, 800 Second Ave., New York City, N.Y. 10017; (800) 221-9831.