There is probably no more battered transit rider than the one who ventures forth daily in New York City.

The legendary subway is now legendary more for its unreliability, filthiness and crime than for the remarkable people-mover it continues to be. City buses are known for collapsing on the streets.

A rising water table and deteriorating concrete have greatly jeopardized parts of the subway trackbed. At the Essex Street Station, for example, trains are restricted to speeds of 10 mph, and surveyors check every day to make sure that the rail has not shifted dangerously on a roadbed consisting primarily of water and temporary wooden blocks. Trains are routed to sidings from signal towers using turn-of-the-century equipment and filling a room that might have been painted last when the equipment was installed.

Rail yards and bus garages are in ruins. Walls have been propped up at a rail yard to keep them from collapsing on workers, and the corner of a major uptown bus garage is supported by a temporary wooden post.

Some of the gigantic electric power substations, where juice from Consolidated Edison is made palatable for the subway's direct-current, 600-volt third rail, are using giant rotary converters that look like a backdrop in an early version of Frankenstein. Electricians who grew up working for the subway system claim to be the only persons on Earth who know how to operate and repair the converters.

Commuter railroads taken over by the Metropolitan Transportation Authority have inspired brilliant writing in New Yorker magazine. Trains on one of the most famous, The New Haven, have recently developed the distressing habit of showing up with broken axles, a problem requiring that they be inspected every 30 miles while passengers cool their heels. Nonetheless, the Big Apple's trains and buses carry almost one-third of the 8 billion trips made by transit riders in the United States every year, and they carry 90 percent of the 1.5 million persons who enter New York City's central business district between 7 a.m. and 9 a.m. every weekday.

Only Chicago's downtown area, at 70 percent, comes close to having that percentage of transit riders. Washington's central business district, in the heart of what is considered a good transit city, draws 34.4 percent of its daily occupants from trains and buses.

Thus, if the New York transit system slides into oblivion -- and the cost of restoring it is estimated at $14 billion over 10 years -- it will take Manhattan Island with it. There is simply no room for both automobiles and skyscrapers.

New York is transit's capital in the United States, and the New York story is being repeated on a smaller scale nationwide. The story is not as hopeless as it seems at first glance: actually, things are better in the New York subway and generally in U.S. transit than five years ago, largely because of a major infusion of federal money.

The question has become whether transit systems, facing deep cuts in federal aid at a time of local economic trouble, can continue climbing out of the ruins and even expand into Sun Belt cities that have suddenly discovered they can handle no more automobiles downtown. Both Houston and Los Angeles, which compete for the championship in admiration of the motorcar, are actively seeking federal aid to build rail systems.

The American Public Transit Association (APTA), which lobbies hard for transit aid, estimated in recent congressional testimony that $50.1 billion will be needed over the next 10 years to meet transit's capital needs. That includes a few new rail systems and replacement of existing bus and rail equipment nationwide.

Meeting that total would require an average annual expenditure of $5 billion. However, federal capital assistance totaled $2.5 billion this fiscal year and is projected to drop to $2.3 billion next year. Thus, most transit authorities are trying to figure out how they will pay necessary expenses as the federal government reduces its role and its money in local transit systems.

In Cleveland, for example, general manager William C. Lahman operates a mix of buses and trolleys plus a high-speed, Metro-style rail line from downtown to the airport. People use Cleveland transit about 298,000 times on an average weekday, and Cleveland residents approved a 1-cent sales tax to support the system.

With hard times, however, that tax is not producing enough to meet expenses and invest in the future, even though the basic fare is 85 cents and the airport train and express buses cost $1. Things are so tough that the transit union recently accepted an 18-month freeze on wages with no cost-of-living increases.

Cleveland has 30 new trolley cars, purchased mostly with a federal grant, but the cars on the rail line, Lahman said, are at least 20 years old and "either need rebuilding or replacing."

Substantial work is needed to improve stations, track and roadbed; the major rail maintenance facility is "badly deteriorated," and buses in the fleet average 10 years of age instead of the preferred seven. The transit schedule was reduced earlier this year for lack of reliable vehicles.

The bill to restore the system to health is estimated at $350 million -- nothing compared to that of New York--but Cleveland does not have New York's financial strengths. "We'll just have to concentrate on the highest priority items," Lahman said.

Similar stories are found in systems big and small. Transit interests in Washington have been trying to persuade the Reagan administration that only federal money can cure such major problems and that transit has a legitimate claim to the money because of the role it plays in city life.

"There is a federal stake in the well-being of our cities," said Jack Gilstrap, executive vice president of APTA. "It's not just a welfare stake, a stake in providing for the needy; transit makes these cities work properly. Cities that don't work are not competitive in the international market."

Gilstrap said he feels that APTA has made progress in persuading the administration of those facts. There has been little difficulty with Transportation Secretary Drew Lewis, who comes from Philadelphia and knows, for instance, that the Schuylkill Freeway -- even after rebuilding -- will never get those who live along the old Pennsylvania Railroad's Main Line to work on time downtown. Trains, subways and trolleys will be a necessity.

Official Reagan policy is to concentrate federal aid on large capital expenditures, such as new subway cars or buses, for existing transit systems. But there are to be no new rail systems and federal aid to operate buses and subways, all of which run at a deficit, is to be eliminated.

Lewis' proposal for a 5-cent gasoline tax increase would include 1 cent for transit aid that must be spent on new subway cars or buses. Reagan has said the proposal is under discussion, and it is clear that the administration speaks with one voice in opposing federal aid that could be used for such operating costs as salaries.

Such aid was cut from $1.2 billion in 1981 to $1.1 billion in 1982 and is proposed at $672 million in fiscal 1983, but Congress is balking as impacts of those cutbacks become obvious.

Because of formulas through which federal aid is distributed, those cuts have hurt less in New York than in Tucson. In New York, federal operating aid represents only about 7 percent of the total transit budget; in Tucson, it represents 20 percent. No matter the size of the budget, it is easier to absorb a 7 percent loss.

Transit's major problem is its eternal balancing act between fares and ridership. In times of rising prices for gasoline and downtown parking, ridership increases almost without regard to fare levels. When gasoline prices stabilize, however, transit ridership tends to drop. Then, even a small fare increase lowers it further.

National ridership climbed steadily through the late 1970s, according to APTA, but reports from many systems this year show it is dropping, perhaps another indicator of national economic difficulty. "We have found over the years that our ridership relates more closely to the number of people working in Manhattan than to anything else," said the New York MTA's Arthur G. Perfall.

New York's ridership is also its future, because fares--along with federal, state and city grants and other revenues -- are pledged by MTA to retire bonds needed for a $7 billion, five-year capital improvement program approved by the legislature last year.

The plan may enlighten other transit systems because it relies heavily on New York's own resources, plus a device in federal tax legislation that lets transit authorities sell and lease back their new buses and rail cars. Private businesses that buy them can claim annual depreciation as a tax writeoff that the not-for-profit MTA could not take.

That device, known as safe harbor leasing, is a form of federal subsidy but makes it possible to buy new transit vehicles without waiting for federal grants.

The plan was conceived primarily by MTA Chairman Richard Ravitch, a builder and developer installed as chairman in 1979 after it became obvious that business as usual would result only in a strangled city.

Ravitch documented the $14 billion projected cost, then set out to show how badly needed it was.

He led state assemblymen and reporters on tours of subway tunnels and yards to underline the problems.

"The Norman Vincent Peale approach doesn't work," said Ravitch, referring in an interview to the advocate of positive thinking. "You've got to build a constituency, be precise about the costs and facts and then go out and sell it."

Ravitch adopted an operating philosophy that, rather than cutting maintenance for budgetary purposes, fares would be raised.

About 2,500 new mechanics were hired, and contracts were negotiated that eliminated a quota system under which a union mechanic's work day was finished after he had lifted his wrench a certain number of times.

The capital plan was designed and approved in such a way that Ravitch has almost blanket authority to go forward, without having to refer each project to state and local politicians for approval.

Emphasis is devoted to making the system appear safer: well-lighted off-hours waiting areas are being established in each of the city's 458 subway stations, yards are being fenced to keep the city's celebrated graffiti writers from attacking the exterior of freshly painted subway cars and new graffiti is removed. Interior graffiti, however, must be dealt with later.

New subway cars are on order, and switches, yards, towers and bus garages are being replaced or repaired, some after decades of neglect.

"There were three choices for us," Ravitch said. "The state could have given us give us the money to fix it; they could have let us borrow the money, or we could continue what we were doing."

That was permitting the subway, buses and commuter railroads to collapse of neglect.

It is possible that, if no additional state subsidies are made available, servicing the debt on bonds sold for improvements could mean as much as a 20-cent increase in the 75-cent fare.

The question to be answered over the next two or three years is whether Ravitch's overhaul can save the system before its creaking structures collapse, resulting possibly in a major accident. Ravitch said he thinks that the turnaround will come in time, that disasters have been averted.

Hugh A. Dunne, a special assistant for operations who led a tour of the system, expressed concern, however.

"As operators," he said, "we worry about water in the tunnels; we know it could make the tracks shift. On the older subway cars [some date to 1948], we know the wiring systems have never been replaced, we know they're fragile. What would happen if they would give out on a hot day in a river tunnel and a train would stall?"

Inferred but unspoken was the subway operator's greatest fear: fire in a crowded train that cannot be moved to a station.