President Reagan's 1986 budget would cut a wide swath through many of the largest domestic spending programs and, in doing so, significantly affect the federal government's relationship not just with the poor but with the middle class and powerful sectors of the economy as well.

From health care to agriculture, from college students to military veterans, the new budget charts a course through the economy that rivals the reductions Reagan achieved in his first budget four years ago.

If enacted, the new budget would begin to take government out of some areas, like farming, and put it more deeply into the operations of others, like medicine. At the same time, it would force state and local governments to assume greater responsibilities, continuing the transfer of power that has marked this administration's philosophy from its first days.

Here is how the president's proposals would affect six broad areas of federal activity: Aid to State, Local Government

Governors and mayors, who absorbed a major share of Reagan's 1981 cutbacks, would lose still more of the federal aid on which they have come to depend. When Reagan came to office, the federal government provided about one-fourth of state and local revenues. Today it is less than one-fifth.

The administration argues that the states' fiscal health has improved markedly in the last two years; local officials counter that they cannot generate new jobs and economic development without this assistance from Washington.

Federal grants-in-aid to localities would be cut from $107 billion this year to $100.6 billion in 1986 and would remain frozen at that level for the following two years.

Reagan would eliminate general revenue sharing ($4.6 billion), an extraordinarily popular program for 40,000 localities. He would kill Urban Development Action Grants ($440 million), which cities use to finance hotels, convention centers and other downtown projects. And he would cut community development block grants by 10 percent, to $3.1 billion, while shifting some of the aid from cities to rural areas.

Mass transit operating subsidies, which many big cities depend on to keep fares at reasonable levels, would be ended at an initial savings of about $700 million. Elimination of Amtrak rail subsidies would save $574 million, and federal highway aid would be frozen, at about $13 billion, for two years. Block grants to the states for health, social services, education, job training and energy assistance also would be frozen. Aid for urban parks would be dropped.

Job training funds for the states, which Reagan has already reduced by about four-fifths, would be frozen at $1.9 billion. There would be rescissions in funds for summer youth jobs and dislocated workers.

Other grant-giving agencies such as the Economic Development Administration and Appalachian Regional Commission would be eliminated, as would community services block grants. Juvenile justice and delinquency prevention grants also would be dropped.

Some of the proposals would have a delayed impact. Nearly every community, for example, relies on the Environmental Protection Agency's construction grants to build costly wastewater treatment facilities; Reagan would freeze the program at $2.4 billion but submit legislation to abolish it.

Operating aid to local public housing authorities, already in fiscal distress, would be cut $240 million, to $1 billion. Available cash to repair aging projects would be reduced by about three-quarters, and subsidies for thousands of vacant apartments would be cut off.

The proposals amount to half of Reagan's New Federalism -- returning responsibility from Washington to states and cities -- without providing the revenue sources as promised in the original plan. Local officials say they also will be forced to fill the gaps left by Reagan's cutbacks in aid to the poor. Health

The president, while generally opposed to government regulation, last year began to impose strict limits on the way the government pays for hospital care in an effort to slow the astronomical growth in federal health care costs. His 1986 budget would accelerate that trend, sharply curtailing Medicare and Medicaid, the giant health programs for the elderly and the poor.

Reagan would hold Medicare outlays in 1986 $4.2 billion below what would be spent under existing law. Over the five years from 1986 to 1990, the projected savings would swell to $43 billion, largely by slapping statutory limits on how much Washington will pay.

The government has established payment ceilings to hospitals for a range of services provided under Medicare. The new budget would freeze those rates, rather than allowing an inflation escalator as originally planned. Reagan also would freeze Medicare rates for payments to physicians, home health care, skilled nursing services, clinical laboratory fees and direct costs for training interns and residents.

On the benefits side, Medicare patients would be charged $4.80 for each home health visit beyond 20 a year. The monthly premium that Medicare patients pay for doctor-insurance services (Part B) would rise from 25 percent of the program's cost to 35 percent by 1990. Medicare would become the secondary payer for workers over 69 who are covered by employer health plans.

In the federal-local Medicaid program, Reagan would "cap" federal payments to the states at $1.3 billion less than they would receive under current law, then limit future payments to the rate of medical inflation.

The reductions would be about double those in Reagan's first term. At that time, many states were forced to cut services and exclude some recipients. A $300 million "antihardship" fund would help states make the transition next year. Projected Medicaid savings by 1990: $17 billion.

The National Institutes of Health would be cut $287 million, reducing the number of research grants from 6,500 to about 5,000. The National Service Health Corps would be cut by one-third, and aid for health professions training and health planning would be abolished.

On paper, block grants to localities for such services as maternal and child health, mental health and drug and alcohol abuse would be increased slightly to $1.6 billion. But these grants would incorporate three previously separate programs -- family planning, migrant health and black-lung clinics -- so there would be no actual increase. The Poor

Low-income families, who were hit by sweeping reductions in Reagan's 1981 budget, would find their aid frozen in many cases.

At the same time, major federal cutbacks in Medicaid and public housing, for example, would increase pressure on local governments, which run the programs, to curtail services to the poor.

The same is true in Aid to Families with Dependent Children, the main cash welfare program, which would be cut by $180 million by freezing administrative grants to the states that run the program. In addition, unmarried minor mothers would be barred from leaving their parents' home to qualify for benefits, and payments to able-bodied parents whose youngest child is 16 or over would be eliminated.

Reagan would cut child nutrition outlays by $654 million by dropping a cost-of-living increase in payments for school breakfasts and lunches, and by excluding those who earn more than $19,000 for a family of four.

The president again would try to abolish the Legal Services Corp., which provides legal aid to the poor, at a saving of $282 million. The Job Corps, which trains young workers, would be killed, saving $1.3 billion over three years. The work incentive program, which helps prepare welfare recipients for jobs, also would be dropped.

Low-income energy assistance would be frozen, at $2.1 billion, as would black lung benefits for disabled coal miners.

Having already halted most subsidized housing construction, the administration is proposing in this budget to sharply scale back rent vouchers to the poor, from 100,000 to 3,500, while maintaining a freeze on rent subsidies.

Reagan would drop the politically popular grants to build housing for the elderly and handicapped, which financed 14,000 units this year. Rehabilitation grants to fix up rental apartments and a small housing program for Indians also would get the ax, as would the rural housing program and most rural development loans.

Savings on subsidized housing outlays would reach $14.8 billion over three years. Education

The student loan program has become one of the most rapidly expanding benefit programs as many middle-class families have come to count on federal help in paying for college. Reagan would cut the aid by nearly one-fourth, arguing that the program helps too many affluent families send their children to expensive schools.

The president would cut budget authority for student financial assistance and guaranteed student loans by $2.3 billion, to $6.3 billion, next year. He would impose a cap so that no student could receive more than $4,000 a year in federal aid. All students would be required to provide at least $800 toward their education.

Reagan would cut off grants, direct loans or subsidized jobs for students from families whose adjusted gross income exceeds $25,000. If that adjusted income tops $32,500, the student would be eligible for a federally guaranteed loan, but no other subsidy.

The interest rates on $7.5 billion in guaranteed student loans projected for next year, now 8 percent, would rise to market levels. And new rules would tighten up on students who claim financial independence from their parents.

Federal grants for handicapped, compensatory, vocational and adult education would be frozen at current levels. Impact aid to communities with large numbers of federal employes would be cut from $747 million to $635 million. ? Veterans

The growing number of veterans over 65, which is expected to double during the 1980s, is putting more and more strain on the Veterans Administration's health care facilities, with total spending for veterans reaching about $27 billion.

Reagan would reduce the strain by imposing a means test on veterans over 65, a move likely to provoke a sharp protest from the politically powerful veterans lobby.

The president's plan would limit free VA health care to veterans over 65 with incomes under $15,000, except for those with service-connected disabilities. While VA health costs would drop $413 million next year, total savings would reach $3.2 billion by 1988.

Reagan also would cut budget authority for construction of new VA hospitals and nursing homes by $157 million, to $612 million. This is significant because the VA must provide free care only if it has the beds available. In addition, private insurance companies that cover veterans would be required to reimburse the VA for their care.

Fees charged to veterans who utilize VA housing loans would be increased from 1 to 5 percent of the mortgage, except for those with service-connected disabilities. Agriculture

Reagan is proposing a dramatic reduction in the farm support programs that have been the foundation of the government's link to farmers since the Great Depression.

The proposals, coming at a time when many farmers face a credit crunch that could throw them into bankruptcy, are likely to be the source of controversy in Congress this year.

His plans would cut outlays for farm income stabilization from $18.3 billion in the current fiscal year to $10.9 billion in fiscal 1986. Over the period of fiscal 1986 to 1990, the changes would reduce the estimated $73 billion in outlays by $39 billion.

Reagan wants to alter the two key elements of farm programs, the price support loans that help put a floor on commodity prices, and the so-called "target price" system, which is used to help calculate direct payments to farmers. The administration wants to tie both more closely to market prices, thus forcing farmers to obtain a greater share of their income from the market.

The administration argues that the changes will bring supply into balance with demand and thus reduce the need for the government to pay farmers not to produce, while reducing artifically high prices, thereby encouraging exports.

Federal subsidies for crop insurance, under which loans are expected to reach $10 billion next year, would be phased out by 1990, putting the program on a "pay-as-you-go" basis.

Emergency disaster loans would be made only where federal crop insurance is not available. The Soil Conservation Service's watershed program would be eliminated. And agricultural extension programs, which provide assistance through county agents, would be cut from $342 million to $267 million.