For months, headlines have been blaring the saga of the dizzying decline of the U.S. dollar: "Dollar Drops Again Against the Japanese Yen." Or, "Dollar Hits New Low Against West German Mark: Gold Hits New High." Or, "Tourists on Holiday Find Their Dollars Buy Less and Less."

What has happened to the once almighty dollar to account for a loss in the past few years of about half of its value against the West German mark, 55 to 60 percent against the Swiss franc, and 35 to 40 percent against the Japanese yen?

The answer is relatively simple, and it's the same one that often applies to a decline in the price of any commodity: an oversupply. There are too many dollars in the hands of foreigners - or at least more than they want to hang on to.

Experts estimate that individuals and central banks of governments abroad hold about $600 billion, much of it pumped abroad to pay for accumulated U.S. balance of payments deficits. Over the years, when this country has bought more goods and spent more money abroad than it takes in from foreign sales and investments, the gap has been covered by printing additional dollars.

The United States has the advantage of being able to do this because the dollar has been not only the chief reserve currency but also the world's chief transactions currency.

As Britain's chief economics official in Washington, William Ryrie, said recently, "The United States does not have to find foreign currency to pay for a deficit in its balance of payments if it has one. The U.S. pays in dollars. The rest of us play in dollars, too, but we cannot print them."

When there is too much of a currency outside the country that issued it, the people who hold it start to lose confidence.

"TThey naturally start to dump them," Henry Kaufman, chief economist of Salomon Bros., New York, said in an interview.

"All you have to do is to create some question marks or fears about the dollar, and if you loosen a fraction of that sum - say just 10 to 20 percent - you have enormous amounts of money that want to get out of dollars into other currencies," Kaufman said.

The situation has become increasingly tense in the past few weeks, with inflation rates in the United States soaring far over those of its major trading partners, West Germany and Japan.

Compared with a 10.4 percent U.S. rate in the first six months, the Japanese inflation rate is 4 percent, and the West German rate is less than 3 percent.

The failure of the economic summit meeting in Bonn in July to come directly to grips with the dollar problem was a great disappointment in financial circles.

In little more than a month since then, the dollar has drifted down 3 to 4 percent against major European currencies and 8 percent against the yen. Such changes over a relatively short time are characterized by veteran market observers as near-chaotic.

Interviews of officials, bankers, businessmen and others here and abroad indicate that the slide of the dollar has reached crisis proportions and that this carries with it a threat to the international monetary system and to world economic stability.

President Carter implicitly recognized that last week by directing Secretary of the Treasury W. Michael Blumenthal, working with Federal Reserve Bank Chairman G. William Miller, to recommend new actions to set the dollar on a steadier course.

But no one - here, in Bonn, Tokyo or New York - thinks that there are any simple solutions.

"Gauging when the critical point will come is beyond any of us," said Robert V. Roosa, partner of Brown Brothers Harriman, in New York.

In a strictly technical sense, it is clear that the dollar already has dropped too far too quickly, and hence is now undervalued.It would tend to rise naturally, economists say, if the U.S. government made a believable effort to control inflation and reduce its massive $30 billion trade deficit.

But the accumulation of worries, the panic psychology of markets "and the natural reaction of holders of assets of seek diversification in the face of steady decline," nonetheless is pushing the dollar further down, Roosa said.

It remains unclear whether the Carter administration, with an unsteady record so far of managing the U.S. economy, can do anything that will restore confidence. A boost in the Federal Reserve Board's discount rate on Friday was welcomed by the markets, but they are looking for much more.

Rossa, under secretary of the treasury in the Kennedy administration, confesses that a year ago he would have thought that if the dollar reached the low rate it is currently at, "we would already be in the midst of a great crisis. The fact that it has happened in wave-like spasms has in part conditioned the rest of the world to it."

The dollar has been in a steady decline for more than a year, but the Carter administration has been reluctant to take decisive action to stop it.

A cheaper dollar has some advantages for the United States. It makes American exports less costly. This not only helps reduce the staggering American trade deficit, but also stimulates U.S. production, sales and jobs.

But it also adds to inflationary pressures at home by boosting the price of foreign goods and making foreign travel more expensive - as tourists paying $3 for a cup of coffee in Japan or West Germany have found out.

Beyond that, however, there are serious problems of economic policy management created for the United States, and this has helped push Carter into seeking new solutions. These problems can be summarized this way:

To protect the dollar and stem the decline, the Federal Reserve is pushing interest rates higher. This provides incentive for dollar-holders abroad to keep their dollars rather than dump them. But a policy threatens economic recovery at home.

A continued slide of the dollar could induce the Organization of Petroleum Exporting Countries (OPEC) to raise the price of oil again. This would be a new deflationary force and could trigger a world-wide recession.

If the dollar dips far enough, this would lower American prestige and political influence abroad. The dollar's role as an international "reserve currency" has already been challenged by others, and a new slide could accelerate the trend.

A dollar decline transfers wealth from the United States to foreign holders. Dollars accumulated abroad are a claim against U.S. wealth. Foreigners today hold about $120 billion in Treasury securities. This transfers $9 billion a year in interest to them.

The reasons for the dollar's difficult situation are many and complex. But most experts agree that the weakness stems from a combination of the rising U.S. rate of inflation and the enormous trade deficit, which last year added some $20 billion to the $600 billion already in foreign hands.

A subtle overlay to these basic reasons is the almost unanimous belief in European, Japanese and other financial centers that the Carter Administration has shown some incompetence in handling its economic problems.Its failure to mount a successful anti-inflation program and to persuade Congress to pass an energy conservation program are viewed with amazement and consternation in Europe.

A cheaper dollar, of course, means that other currencies, like the mark and the yen, become more expensive. This makes goods produced in the countries of the mark and the yen less competitive in world markets.

But if countries like West Germany and Japan choose to halt the decline of the dollar by intervening to prop it up that action leads to a boost in their own domestic money supply - hence, a new inflationary threat to them.

So their demands have been for greater U.S. intervention, by which this country would assume the major burden of responsibility for protecting the value of the dollar.

Steadfastly, the Carter administration has refused the kind of massive intervention that would "peg" the dollar at any fixed rate or range. It believes that such an action would be useless in the face of $600 billion sloshing around in European hands.

Roosa flatly predicted that the dollar will continue to be "battered" in world currency markets because of the hugh supply of dollars abroad. He said the dollar, which at the end of the week was worth only 1.65 Swiss francs, could decline to a 1-to-1 ratio, with additional but less spectacular declines against other currencies.

"Until there is a substained, clear turn in the Japanese current account surplus, I don't see anything stopping [the appreciation] of the yen," Roosa said.

He suggested that the yen - which at the end of World War II and for many years later was 360 to the dollar - could move to 150 to the dollar. Less than three year ago, the yen was over 300 to the dollar.

Kaufman, one of the leading observers of financial markets, said in an interview that merely improving the trade position of the United States would not solve the dollar problem.

"It would help," Kaufman said, "but it won't solve it. The problem goes beyond the current account and relates to the capital account - the international financing role of the dollar."

In effect, Kaufman says, the United States has played the role of international banker and suddenly international banker's currency doesn't appear to be very sound, eroding at a double-digit rate.

In the past, Kaufman pointed out, when a major reserve currency - like the pound sterling - appeared threatened, the central bank of that currency's country raised interest rates considerably, which quickly aborted any dumping.

"But that is very difficult to do in a modern society," Kaufman observed. The tradeoff for high interest rates is usually a depression of business activity and more unemployment at home.

He noted that Miller in the past few months had given markets the impression that the Fed would ease interest rates in the United States or at least not "overstay" tight money.

"The symbol of preserving the integrity of the dollar internationally tends to be in the discount rate," Kaufman observed. But Miller actually voted against the majority of his board in a July boost in the discount rate, from 7.0 to 7.25 percent, something that jarred the markets.

"It was an enormous disturbance in the foreign exchange markets," Kaufman said. Banker David Rockefeller confirmed this assessment, noting that "Miller's vote suggested that he didn't have control" of Federal Reserve policy.

Since then Miller has said that he made a mistake. He voted with the majority on Friday to raise the discount rate to 7.75 percent, citing international as well as domestic reasons.

What are the answers to the problem?

In groping for a response, the adminsitration tends to fall back on its complaint that Congress has ignored the energy legislation, which it considers critical. Interest rates, as the Federal Reserve action last week demonstrated, are moving higher. A more postiive intervention policy, perhaps with greater U.S. resources marshaled for the day-to-day operations, is also possible. Other nations, like West Germany and Japan, although reluctant to do so, may take on more of the reserve currency responsibility.

But inflation remains the key to the dollar crisis. It remains to be seen whether the Carter administration can mount a stronger anti-inflation effort through traditional means like tighter control of budgets, or supplemental measures involving direct or indirect limits on wage and price increases.

What's needed, Rockefeller says, is evidence that the government "is taking effective policy steps leading to a change. The minute it's felt that we're moving in the right direction, the dollar could move up long before things are fully corrected. It's the perceived trend that's important."