AS THE administration experiments with various ways to curb federal spending, the country is receiving many useful lessons about what the federal government really does--beyond generating fraud, waste and abuse. Consider, for example, the president's decision on Monday to close down much of the federal apparatus when Congress failed to produce a government spending measure that he found acceptable.

Mr. Reagan ordered his department and agency heads to furlough all "non-essential" federal workers until Congress reached an acceptable agreement for continuing funding of the government's operations. Exempted from layoff were workers needed to protect life, property and national security. These essential employees included defense and intelligence workers, law enforcement agents, NASA satellite monitors, air traffic controllers, money printers, tax and custom colectors, Social Security claims processors, personnel in veterans' hospitals and keepers at the National Zoo. All the rest were told to go home.

Question: How many federal workers were found not to be absolutely essential? Answer: About 400,000, or less than one in five civilian federal workers.

Another question: How long could most of the other workers be spared? Answer: Probably not very long. If, for example, you were one of the people trying to get a passport in a hurry last Monday, you would have been annoyed to find the passport office closed. So were the people who had come to the nation's capital to visit the Washington Monument and the Smithsonian's museums--the people who man those posts weren't deemed essential.

Farmers wouldn't want to go without their special subsidies for very long, nor would the builders of highways, dams and other popular construction projects. And then there are all the federal workers who process and monitor grants to states and localities for essential services like medical assistance, sewage treatment and air pollution control, food stamps, welfare, unemployment insurance and school lunches. These programs can carry on without continuing federal assistance for a few days, but after that many of them would be out of business.

One might even guess that top White House officials and Cabinet officers would soon tire of answering their own phones, begin to wonder what citizens were trying to tell them over the defunct White House "Comment Line" and long for their chauffeurs.

There are, no doubt, some federal workers among the ranks of both the essential and non-essential-- however classified--who could do their jobs better and faster. But Monday's shutdown was an important reminder--for both the government itself and the public--that most federal workers, by and large, do things that are useful to the society.