Mayor Marion Barry yesterday unveiled an austere 1982 District of Columbia government budget that calls for deep cuts in city services, a sharp increase in water rates, no firm plans for a pay increase for city workers and decreased funding for the city's troubled school system. "This is a good news budget," Barry said, as he described the $1.5 billion financial plan at a District Building press conference. But the budget -- the first prepared since the full extent of the city's budget crisis was revealed -- reflected what Barry has described as a new tone of austerity, and seemed to hold mostly bad news for most Washingtonians.

Barry said the budget reflected his commitment to maintain basic city services, while at the same time balancing the city's budget and beginning to pay back a deficit accumulated over the last dozen years and currently estimated at more than $400 million.

Barry proposed no increases in sales, income or real estate tax rates for the 1982 fiscal year, which begins Oct. 1, 1981. However, the tax bills of District homeowners will increase because of rising property assessments.

Some of the provisions of Barry's 1982 budget will have widespread impact:

A 30 percent increase in water and sewer rates for all city residents and businesses.

A 5 percent increase in payments for persons receiving Aid to Families with Dependent Children or General Public Assistance welfare funds. "It's not enough, but it's a good start," Barry said.

Funding of only $238 million for the D.C. public school system, a decrease of $6 million from 1981 funding levels. Barry said this reduction can be achieved without further layoffs, but School Superintendent Vincent E. Reed said an additional 300 layoffs will be required.

A cutback to once-a-week trash collection in the "outer ring" of the city, including Wards 4 and 7 and parts of Wards 3 and 5. Twice-a-week collection will be retained in the inner city.

A $171 million capital improvements budget that would allow the city to continue the reconstruction of its fast-deteriorating bridges and resurface more streets.

Sharp cutbacks at the city's two chief detention facilities, the D.C. Jail and Lorton Reformatory. Counseling programs will be all but elminated and the staff reduced, including the number of chaplains.

A cut in police department funding, although Barry said no police layoffs are contemplated. Barry also has plans to shut down one of the city's 49 fire companies.

A wide range of cutbacks in other areas like recreation, mental health treatment and tax assessment inspection, as well as shorter hours at a number of District government facilities and a further decrease in the number of District government employees.

Meanwhile, Barry increased funding in some areas other than welfare aid. The Office of Latino Affairs will have its budget more than doubled from $114,600 in the 1981 fiscal year, which began yesterday, to $282,400 in fiscal 1982. Funding for the Commission on the Arts and Humanities will also be increased sharply, from $362,800 this fiscal year to $809,500 for 1982.

The District's annual appropriation to the D.C. Chamber of Commerce, a primarily black small-business organization that was rocked this year by allegations of misuse of funds by a chamber official, will be doubled in 1982 from around $50,000 to $100,000. Receipt of the funds, however, will be contingent on an audit of the group's books.

At his press conference, Barry said the budget maintained a commitment to "basic human rights." He added, "This administration will never abandon those who need us most."

The 1982 budget does contain a $1.6 million increase in District funds for the Department of Housing and Community Development, including funds for the renovation of the decaying Barry Farms housing project in Southeast Washington.

But the aspects of Barry's budget likely to provoke the most discussion are the cutbacks. "When I took office in January of 1979, in my opinion this government had very little sense of priority," Barry said yesterday. The 1982 budget represents his first opportunity to spell out his priorities for the city, with full knowledge of the extent of the budget crisis and the city's long-range financial problem of expenditures growing faster then revenues.

Barry set aside $20 million in the 1982 budget to begin paying off the city's $400-million deficit. Officials said reserving this money, which otherwise could have been used to cushion the impact of some of the reductions, illustrated the administrations's commitment to fiscal responsibility.

The budget proposed by Barry yesterday totals $1.5 billion. However, this represents only that part of the city's operations financed by local tax revenues and the annual federal payment from Congress. Federal grants, which make up a large percentage of the operating budget of some agencies, will balloon the total District budget to well over $2 billion.

Barry's $1.5-billion budget amounts to a 5 percent increase over the current $1.4-billion budget. Barry said a larger increase had been projected initially, but the budget was cut back due to "the constraints of reality."

The budget assumes that the city will receive a $300-million federal payment. The District has never received that amount, although it appears that the payment for the current year will total more than $290 million.

Barry said that the city would seek a fixed-formula federal payment of $376 million as provided by pending legislation introduced by D.C. Del. Walter F. Fauntroy and Rep. Ronald V. Dellums (D-Calif.). If that increase is approved, Barry said, he would then be able to grant city workers a pay raise in 1982.

Public employee unions are already incensed over Barry's decision to offer them only a 5 percent increase this year, and reacted angrily to the prospect of having no pay raise at all in 1982. "That is preposterous," said Robert E. Peterson, president of the Greater Washington Central Labor Council."Can the Mayor control the rate of inflation?"

Barry said that for the city to meet its commitment of a $79-million operating subsidy for Metro bus and subway operations in 1982, it would be necessary to receive the higher formula-based federal payment, to secure permission from Congress to reinstate a tax on non-resident professionals, or win aproval for some other form of commuter tax. Congress and the courts have consistently said no to the District's attempts to tax the incomes of non-residents.

Perhaps hardest hit by the budget are the schools and the Department of Corrections. School Supt. Reed flatly accused Barry of "cutting in a callous way" that undermines the progress of the school system in improving pupil performance and test scores.

Barry said the cuts in the schools were made because of declining enrollment, and said the school board had already identified 22 underutilized schools which could be closed to help cut costs. He said the $6-million cut in school funding would require no new layoffs and would not force the schools to increase class size. But Reed was adamant that both more layoffs and increased class size would result.

The cuts in corrections promise to have their greatest impact on inmates at Lorton Reformatory and the D.C. Jail. Food budgets will be trimmed, psychological counseling curtailed and alcohol and drug abuse counseling eliminated. All chaplains will be phased out and the parole staff reduced.

Despite the cuts in services and staff, the proposed budget contains few major surprises because Barry has been saying for months that such measures were coming. It is clear the Barry administration feels the need to staunch the hemorrhage of deficit spending, a requirement that has overtaken other priorities that were the basis of Barry's policy when he took office. The budget, Barry said, is aimed at balancing his "commitment to basic services" with the need to keep future budgets truly balanced in an age of rising costs for everything from fuel to textbooks.

Though the budget document does not list the sources of anticipated revenue, the process by which it was prepared reflected the new approach that has been forced upon Barry by the circumstances he inherited.

Instead of taking one year's expenditures and simply adding on to them to arrive at the estimate figure for the next year, Barry's aides figured out how much revenue will be available and worked backward from that.

They calculated that they would have $1.5 billion in general fund revenue in 1982, mostly from local taxes, to carve up; if they had prepared the budget the old way, routinely assuming a certain percentage of growth, it would have called for expenditures of $1.7 billion instead of $1.5 billion, and there would have been an increase of $200 million in the cumulative deficit unless taxes were raised enough to cover the difference.

Budget Director Gladys Mack also calculated that the $1.5 billion available, $594 million, or well over a third, was committed in advance to obligatory expenditures such as the Metro subsidy, welfare, debt service and pensions. That left only $906 million over which the mayor had control, and he had to parcel that out in a way that would blame the demands of voters, Congress and creditors.

The budget provides for an addition of 54 persons to the staff of the Office of Financial Management. Their job will be to operate FMS, the new computerized Financial Management System, which was ordered by Congress to bring order out of the chaos of the city's bookkeeping. Having no choice, Barr had to add those 54 white collar workers to the proposed payroll even as he was laying off low-income workers in other departments.

The spending plan that resulted from these considerations, Barry said, "is not the kind of thing I would be doing if I could make the world over again," but it reflects "the discipline and rewards of an independent government" living within its means.