MARTIN KRIEGER LEFT his home in Durham, N.C., in March for the Raleigh/Durham airport, went to Pittsburgh, flew to West Palm Beach, on to Minneapolis, east to New York, down to Philadelphia and then back home.

His two-week trip, arranged primarily to see friends and family, cost $249 using USAir's "Liberty" fare.

Without the special promotional fare, the same trip -- excluding Pittsburgh, which was used solely as a connecting point -- would have cost about $591.

USAir's Liberty fare, introduced during the bicentennial year, allows a person to fly almost anywhere on the expanding airline's system within 15 days for a specific price. The fare would have been $399 had Krieger wanted to include Phoenix or Tucson, the most western cities on USAir's route system, on his itinerary.

Despite the fact that the Liberty fare has just gone up -- to $279 and $449 for the two options -- it is just one example of many special promotional fares available that allow travelers to cut flying costs considerably if they are willing to take the time and trouble to research their options.

Overall, air fares -- like everything else -- are going up. Along with the inflationary pressures any other business faces, the airlines are particularly hard hit as well by the unprecedented escalation in the cost of jet fuel. Prices of the lifeblood of the aircraft have more than doubled over the past year. For instance, Eastern Airlines found itself paying $253 million for jet fuel in the first three months of 1980, $133 million or 111 percent more than it had paid in the same quarter of 1979, even though it held the increase in kerosene consumption to 4 percent.

But while costs have gone lup, and air fares have followed, they haven't uniformly followed at the same rate. Although the Civil Aeronautics Board has granted increases of about 30 percent in allowable fares over the last year to the airlines, the average fare being paid by travelers has risen by half that. The reason is that about 50 percent of all domestic passengers are now flying on discount fares, according to the CAB, as airlines seek to lure them to fill otherwise empty seats.

As a result, there are innumerable promotional fares: family fares, three-for-less-than-the price-of-two fares, kids-fly-free fares, super savers, super value, super jackpot, unlimited mileage, Saturday flight sales, senior savers, simple savers, moonlighter, good buys, group fares. The fares are in addition to the games being offered until May 10 by American, Trans World, and United airlines who hope to lure passengers to their flights instead of a competitor's.

Generally, the games give odds of something like 325 to 1 that a passenger (or player by mail) will get a game card entitling him or her to a free roundtrip flight. Until May 14, National Airlines is giving travelers on its flights to Florida a coupon that entitles two members of a family to fly for the price of one to one of 11 destinations of Pan American World Airways, its merger partner.

The promotional fares have differing rules, such as advance purchase and minimum or maximum-stay provisions or have penalties for cancellations, and they may be complicated, but a little perseverance may turn up a fare that is exactly right for you.

Business travelers, as well as vacationers, can cut down on their flying costs by being aware of, and receptive to, the unrestricted lower fares of the airlines that have recently entered the industry or a new route, courtesy of the freedoms given them under increasing airline deregulation.

For instance, World Airways, the former charter-only airline, announced a $140 one-way fare to the West Coast from Baltimore (and $240 each way from here to Hawaii) from May 15 to the end of the year.

There are no advance purchase or minimum or maximum-stay provisions and the fare applies to all seats on World's flight. It announced fares are well below what the major airlines on those routes had been charging. Although the majors may seek to meet this competition, their unrestricted one-way fares during the spring between Baltimore and Los Angeles were about $250 each way at night and $310 during the day. Fares with restrictions could lower the price significantly, of course.

World had been flying at $193 each way when it resumed service in February after a lengthy strike. Flying admittedly inadequate numbers of passengers, World effectively attracted attention with a rock-bottom $70 transcontinental fare and a $140 fare to Hawaii, each one-way, for seats on its flights between April 15 and May 15.

When Eastern jumps in from New York to the West Coast for the first time this summer, new cross-country competition may put additional pressure on the downside of fares that could make a trip to New York and then West worthwhile, but it's too soon to know. In addition, numerous other airlines, like Texas International, offer special fares across the continent on their connecting flights.

Air Florida, once just a Florida carrier, is now operating flights from Washington to a variety of destinations -- not just Florida -- and also offers unrestricted fares that are lower than its major competitors' to the same destinations.

As predicted in the textbooks, carriers already in a market have responded to new competition on their routes with lower fare offerings. This winter, the overall fare level between the Northeast and Florida fell with the influx of airlines into the warm-weather state. Besides lowering its fares overall, as did others, Eastern also responded with a commuter passbook that offers frequent travelers a coupon book for a specific price that allows an indefinite number of flights to and from Florida for a 30-day period.

Midway Airlines, a brand-new carrier operating since the fall from Chicago's Midway Airport to Detroit, Cleveland and Kansas City, will soon hit the Washington area with its low unrestricted fares. Seats on its flights between Washington National and Midway beginning in June, will cost about a third less than the unrestricted fare on planes currently flying into busy O'Hare International. Besides the fare savings, the traveler can avoid the congestion at O'Hare that anyone without a connecting flight should love to avoid.

Saving money on traveling today requires vigilance; watching newspaper and other advertising is essential, and paying attention to word-of-mouth travel gossip is valuable. Check around. There are innumerable fares that might apply to your plans or your dreams. Don't be afraid to ask, "Is there a cheaper way to get there?"

There's no telling what you may turn up.

For instance, Pan Am has been offering a cheap standby fare from New York to the West Coast for a long time; the fare just went up to $135 each way after holding for a long time at $100. While Pan Am doesn't elaborately advertise the fare, PA officials say they aren't aware of anyone with a standby ticket being turned away from one of their flights because it was full. Everyone has been accommodated, so far at least, they say.

Sometimes, an airline will drop a fare, as Swiftair did recently in California, to introduce passengers to a new plane, in Swiftair's case to its new Fokker F-27.

Although the "almighty dollar" isn't what it once was abroad, it can bring foreign trips more in range for those willing to find out about attractive fares -- which are always changing as airlines start new routes. World, for instance, won CAB approval over four other airlines last month to begin service between Boston and London June 1, with a promise to offer an unrestricted fare at about half those now being charged. The airline also plans to begin its London-bound flights from Baltimore, allowing Washington-area travelers single-plane service and perhaps putting some downward pressure on other airlines' fares.

If Britain is your destination, don't forget Laker Airways out of New York. Freddie Laker started some pretty intense fare competition across the North Atlantic almost four years ago when he started the no-reservations, low-fare "Skytrain" service. Laker now offers several different fares, however. The long lines once associated with Laker are gone. Now, the airline can book a reservation for the next available flight to anyone who shows up to purchase a standard Skytrain fare, which is still Laker's lowest -- $363 roundtrip this summer, $342 roundtrip now.

If Europe is your vacationland, don't overlook Icelandair out of New York. Seek information on charter flights as well. Though not as prevalent as before, they're still around and travel agents should know about them. One source is the Council on International Education Exchange (205 East 42 St., New York 10017, phone 212-661-1414). CIEE offers charter flights -- most of them available to the public -- from New York to Paris, Amsterdam and Tel Aviv. CIEE also guarantees the fare; once the purchaser has the ticket, the price won't be altered. The CAB is currently considering proposals from many airlines to abandon that same practice in the scheduled market.

Check all the airlines flying to a destination. If you want to go to France, check Air France as well as the U.S. airlines that fly there. Air France -- which operates the most expensive flights to Paris on the Concorde -- also introduced "Vacances" promotional fares that were met by TWA. And just as the U.S. airlines offer foreign travelers special fares to travel within the United States, foreign airlines offer similar "passes" in their countries. For instance, Air Inter, France's domestic airline, offers unlimmited air travel to 30 French cities for $177 a week, $275 for two weeks.

Has a trip to Brazil always appealed to you? Braniff Interntional is introducing its new nonstop 747 service from Miami to Brazil on June 1 with fares as low as $572 roundtrip, with various restrictions.

Should a trip to Japan be your dream, besides the U.S. airlines flying there check Japan Air Lines. JAL has introduced some advance-purchase excursion fares, too, which provide discounts of a third off normal economy fares. If you're a college student, JAL is offering for a first time a 17-day tour of Japan that combines a group air fare with accommodations in minshuku, popular Japanese guest houses.

Travelers will find airplanes generally much more crowded than they used to be. With the increased competitive pressures and escalating costs, airlines must fill a greater percentage of seats to make money than previously. Also, some scheduled airlines have been adding seats to existing planes when possible to gain more capacity -- and more paying passengers per flight -- much as charter airlines have done traditionally. This also allows them to increase seating capacity without buying the expensive new planes.

One caveat: the airline industry has become dynamic, and fares and routes are always subject to change. It's possible that, by publication date, many fares listed here may no longer apply. Travelers may be interested in taking a look at a new magazine called FareSaver, a monthly guide to domestic discount air fares that is being produced locally. The publication includes 2,000 point-to-point listings including the 1,000 largest domestic city pairs. Single copies are available from the publisher for $5 prepaid (Airfare Publishing Co., P.O. Box 40944, Washington, D.C. 20016).