Want to save a lot of money on your next trip to California? Go to Richmond and back tomorrow.

Thanks to United Airlines' innovative "Half-Fare Coupon" plan designed to lure customers back after its crippling two-month strike, short trips taken now can yield big savings no longer trips later.

For instances, a passenger who takes a trip to Richmond and back soon will obtain two coupons which may be used to buy two round-trip tickets to California-or anywhere in the continental U.S. on United-for half the regular coach or first-class fares.

The savings can be substantial. For example, by spending $62 round trip on a flight to Richmond-United's shortest hop from here-a traveler will get coupons that allow two persons to save a total of $468 on two round-trip tickets to San Francisco. The coupons allow each person to buy a ticket for $234, half the normal economy fare. That's two tickets for the price of one.

American Airlines has matched the United plan as well. Its shortest hop is to Philadelphia.

Of course, discounts are available that can bring the price of air travel to half the normal economy fares, but they involve often complicated restrictions and careful planning. For instance, a traveler this summer could get to San Francisco from Washington for $234 without the half-fare coupons. But the traveler has to go night coach Super Save midweek: after 9 p.m. but before 7 a.m., Monday through Thursday, buying the ticket 30 days in advance, staying between 7 and 45 days, and only if the seats are available.

Other discount fares to San Francisco range to $328 round trip.

The half-fare coupons are good on any flight with no restrictions, subject to the same availability as regular full-fare customers.

Here is how it works:

Now through June 17, every passenger on every United and American flight gets a discount coupon. If a passenger goes to one city and changes planes, he or she gets another coupon on the second leg of the trip as well. The passenger gets a coupon whether traveling on a first-class, coach or discounted ticket.

During this first three-week period in which United is getting back into operation, it also has approved from the Civil Aeronautics Board to accep the Super Saver and other discount tickets written by other airlines, something usually not done. Ordinarily, airlines accept just the full-fare tickets of other airlines.

The discount coupons entitle the holder to buy a ticket for air travel on United of American at 50 percent of the regular fare for travel originating on or after July 1 and completed on or before Dec.15. One coupon can be used for a round trip, a circle trip (involving more than one stop) or a trip with an "open jaw," for instance, going to Los Angeles from here, driving to San Francisco and flying back from there.

Once a portion of the ticket purchased with the coupon is used, no route changes will be allowed.

"It was a very smart thing to do," says one CAB official about the United plan. "It spreads their afterstrike losses to more months than one. They had no reservations booked and they didn't want to operate three weeks empty. This spreads the cash-flow consequences over a longer period of time."

The coupons also are freely exchangeable. As an american Airlines reservations agent said yesterday, "You can use them, give them away or even sell them."

The half-fare coupon plan was proposed by United for just the first three weeks after it resumed service, which was on Monday. More flights are added each day, and a United spokesman said the airline plans to be back in full operation by next Monday.

United also proposed a $108 one-way fare between New York and Los Angeles to compete with the scheduled service began in April by World Airways, formerly a charter airline. The one-way coach fare had been $236.

Yesterday, World officials charged that United's plan to charge the same fare, matched by Trans World Airlines and American, was a form of unfair competition, was predatory because it must be below their cost, and was discriminatory because United still would be charging some passengers on the route regular coach fares.

"The purpose of this is for these Goliaths of the industry to drive out this little David," Peter N. Teige, a World vice president, complained.

A spokesman for United said that World was mistaken-that the new price for every coach seat would be $108 and that no one would be charged more.