Fare wars in the airline industry since deregulation have produced a bonanza for travelers willing to spend the time it takes to find the lowest price for the trips they want to make.

It can take time -- time to get information and time to take advantage of off-peak bargains, inconvenient layovers and connections and out-of-the-way airports. But right now, because of the competition among carriers, the savings for air travelers can be substantial:

Here are two examples:

*A man I know was planning a multicity trip from Washington to Houston to Dallas to Minneapolis and then back to Washington. He was told by his travel agent that the lowest possible price would be about $600. But after doing some additional research on his own -- by calling several airlines and talking to friends and relatives who had made similar trips -- he was able to get the price down to $350. Most of the savings came on the Minneapolis-Washington leg of the trip, which would have cost about $244 to $254 on major airlines making that run. But through a Minneapolis relative, the man learned about a $131 fare offered by Continental Airlines -- an airline that wasn't mentioned by the major carriers.

*Recently, when I traveled from Washington to Houston, I was able to book a flight on a cut-rate airline for $85 by traveling on a Saturday and accepting a routing that required a two-hour layover and a change of planes. Major airlines typically charge $150 to $300 for that trip.

"There are tremendous bargains for travelers who know how to take advantage of the system," said Willard R. Brown, vice president of travel services for the American Automobile Association, the largest travel agency in the U.S.

One way to do that, Brown says, is to find a good travel agent with computerized equipment and a willingness to "go through screen after screen of information . . . to search out the best schedules and best fares in keeping with your needs."

But because even the best of travel agents have a tough time keeping up with the industry's complex rates and routings, travelers should be prepared to make their own arrangements when necessary. They will be able to do this better if they know something about the deals, cut-rate prices and price-setting policies of the airlines.

Consider "capacity" pricing.

That is the industry term for the practice of assigning different prices to seats on the same flight. "Suppose we have 100 coach seats on the flight between Washington and Dallas," explained one American Airlines reservation clerk. "We may set aside 30 of them to sell at $139; 30 of them to sell at $269 and the remaining 40 to sell at $315. What happens is that the people who call first get the lower prices; when those seats are sold, we start selling the $269 seats, and so on. What you pay depends on when you call and how many seats have been sold at that point."

In addition, there are the cut-rate airlines that offer bargain fares by using older airports and by routing their planes through central hubs that require travelers to change planes. These carriers typically charge for check-in luggage (carry-on luggage would have no charge) and for food and drinks on the flight.

One example of this no-frills approach to flying is offered by People Express Airlines, which offers exceptional savings to passengers willing to tolerate the confusion and chaos of the New York/Newark Airport and the long layovers there. Also, you must be willing to deal with the frustration of making repeated phone calls to reach People Express on its busy telephone lines.

Here is a checklist of ways to save:

*Watch for news and advertisements about special deals to areas where you may want to travel.

*Make your own arrangements if you think you can do better than your travel agent.

*Ask friends and relatives who live in the area you want to visit what they recommend. They may know of an airline that serves their area that you haven't heard about.

*Travel at off-peak times or at night when prices are lower.

*Consider flights that involve plane changes and layovers. This can take longer, but if you can spare the time, you can save money.