Stockman's lesson: changing Washington takes more than scissors; Government: Is it less than meets the eye?; The Education of David Stockman and Other Americans, by William Greider. New York: E. P. Dutton. 154 pp. $5.95 (paperback).

When Budget Director David Stockman, in the pages of The Atlantic Monthly, let slip his frustrations with the process of governing America, the press corps pounced with a glee normally reserved for Abscam payoffs or the prospects for panda parenthood at the National Zoo. The resulting imbroglio didn't quite shake Stockman from his job, but it did overshadow the complex contents of William Greider's long, reflective article, ''The Education of David Stockman.''

''I had expected, after the original flurry of reaction and controversy, that some attention might be given to the deeper questions raised by Stockman's account of governing. A practicing politician would say that I was remarkably naive,'' recounts Greider.

''The Education of David Stockman and Other Americans'' is Greider's book-length expansion of his article, containing both the original Atlantic piece and the author's latest musings on the mysteries of government, economics, and the media. For those who heard only Stockman's most sensational quotations repeated on the evening news, the book offers a fascinating case study of the ''natural anarchy'' of high-level US public policy decisions.

It begins as Stockman first steps into his position, a former Michigan congressman. He is now convinced that liberal politics has lost the ability to judge the justness of claims on government resources, and so yields to all of them - creating fiscal chaos without real social gain. The new OMB director sees reversing this ''constituency-based choice making'' as his mission. His scissors will snip, not just those programs that are easy to cut, but those that have poor arguments for federal money, Stockman believes.

''The fear of the liberal remnant is that we will only attack weak clients. We have to show that we are willing to attack powerful clients with weak claims, '' says Stockman early on in the game.

But things didn't quite work out that way. Powerful clients such as the Export-Import Bank and the Pentagon shrugged off Stockman's shears as if they were made of rubber. Policy decisions made in haste, such as the package of social security reforms floated in May 1981, proved politically damaging. The ''new magic'' of supply-side economics didn't quite deliver as promised. Deficit projections got bigger by the hour.

''In short,'' says Greider, ''the Reagan administration had trapped itself in the same dizzying arithmetic which had confounded fiscal management under its predecessors.''

What happened? What did David Stockman learn in the Washington school of hard knocks?

Greider concludes, unsurprisingly, that government is simply more unmanageable, full of more ''random elements,'' than Stockman realized when he first took office.

Policy formation was revealed as ''a kind of natural anarchy, a helter-skelter sequence of events normally concealed from public view. Is no one in control, even at the highest levels of power? Is that how government really works? . . . The permanent answer, I am convinced, is 'yes,' '' writes Greider.

Yet he finds this conclusion ''strangely reassuring.''

''The core of democratic possibilities lies in the realization by ordinary people that the political elite who decide things, whether it is foreign policy or budget forecasts, are not so different from themselves,'' Greider writes.

This realization ought to stimulate more direct involvement with the political process by average citizens, he says. But Americans try very hard to elect politicans who are different from themselves, who show ''mythic qualities, '' in Greider's own phrase - an ingrained desire for easy solutions that could make more citizen involvement a difficult thing to come by.

Greider believes successful presidents in the future might publicly acknowledge the uncertainties of governing. ''Perhaps there is a useful source of mystery in humility, if a politician handles it right,'' he says.

But, again, Americans do not seem to treat kindly such soul-baring in a politician. Who offered up a more uncertain vision of the future, after all - Carter or Reagan? Greider seems to be ahead of his time by speculating that ''even in politics, confronting reality rather than hiding from it may prove to be, not merely right, but also smart."