WASHINGTON, March 13— They look neither legendary nor remarkable, but simply middle-aged and neatly dressed. They sit at the switchboard for eight hours each day -more during international crises and snowstorms - and, with a practiced note of friendly firmness in their voice, answer each phone call, ''White House.''

But in Washington the operators and the job they do have taken on legendary trappings. Folklore has it that the White House operators, currently 18 women and two men, some of them there since the Truman Administration, can track down absolutely anyone, no matter how obscure, distant or determined not to be reached.

President Kennedy once demonstrated that point by ordering the operators to find a staffer who, unbeknownst to them, was standing at the President's elbow in the Oval Office. The man was located within minutes. President Eisenhower once had to speak to Clarence Randall, a consultant who was deep-sea fishing. The operators asked someone to nail a note to a tree near his landing spot, and when he came ashore he saw it and called the White House. President Johnson boasted that the operators could find anybody, ''if he's living.''

That, the operators say with quiet modesty, is not far from the truth.

The operators work in a sub-basement suite of the Old Executive Office Building, next door to the White House. The switchboard room is locked. All visitors must be cleared.

The suite is simply furnished and cheery. A large picture of President Reagan posing with all 20 operators takes up one wall. Autographed glossies of Bob Hope and the actor Tom Selleck hang on another. The small room is almost completely filled by the 10-position Western Electric switchboard. It is the old-fashioned kind, with operators using black and red wires that plug into holes corresponding to the 5,000 telephones within the White House complex. The board has been in use since l963, when it was installed to handle the heavy flow of calls that followed the Kennedy assassination. It is ''somewhat outdated,'' according to John F.W. Rogers, Deputy Assistant to the President for Management.

The White House has no plans to update the hardware, however. The current board allows the operators to see who is talking to whom, information that is vital when the President wants to interrupt a call. More advanced systems simply flash numbers on a screen, said Mr. Rogers, preventing operators from keeping track of who is on which line.

Somewhere in the office are the file cabinets full of the thousands of private numbers the operators use to locate their prey. The precise location of the cabinets is a secret, as are their number and the color of the cards on which the numbers are printed. People give them those numbers with the guarantee that they will be kept confidential, the operators say, and they are.

In fact, not even former Presidents can breach the security of the phone room. When former President Carter left office two years ago, his secretary, Susan Clough, called the switchboard and asked for certain numbers so that the President could keep in touch with other world leaders via their private lines. The request was denied. A compromise was reached allowing the former President to call the switchboard whenever he needed help in locating someone, an arrangement Miss Clough says he uses to full advantage.

''I had just moved back to Washington,'' she said, ''and my phone in my new apartment had been connected less than an hour when it rang. It was a White House operator.'' Mr. Carter had called from Atlanta and asked the switchboard to find Miss Clough. ''I asked her how she did it,'' Miss Clough said of the White House operator, ''but she just laughed.''

The phone number files aren't the only closely guarded secret in the switchboard office. The operators agreed to be interviewed only if their names were not used and if they were not asked questions about the current Administration. Their professional techniques, such as how they verify whether a call is legitimate and the proceedure they follow in the event of threatening calls, are secret. How they voted in the last election is also secret, but for different reasons.

Unraveled and laid end to end, the circuitry in the White House switching room would circle the world two and a half times. One and a half million calls a day (17 each second) go through the White House, the Executive Office Buildings and 15 other affiliated buildings, about the normal rate for a city of 70,000 people.

Telephones are so integral a part of the White House that it is hard to imagine that the building once existed without them. The President is never far from a phone, with sets strategically placed in the hallways so he can reach and be reached even as he walks from room to room. The White House phone bill for equipment and local calls alone averages $39,000 each month.

Actually, there are two switchboards serving the President, the regular White House board and the Signal board, manned by the military and used mostly for overseas calls. The Signal Corps sets up all communication for President Reagan when he travels, equipping every boat, plane, car, hotel - anyplace the President might conceivably be - with phones that can automatically connect with the White House.

Not all Presidents used the Signal Corps for this purpose, however. President Johnson, disturbed by the sound of a male Signal Corps officer saying ''Number, please'' insisted that the female White House operators come along to place his calls while he traveled.

''They all work hard, they're all nice to us,'' said one operator of the Presidents who have passed through the White House during her tenure. Most of the operators have been there at least since the Nixon years, some much longer. None could think of a President she didn't like. All said they tended to vote for the incumbent, because they became attached to the man in office and his family. President Johnson used the phone the most, they say, talking from dawn until past midnight. President Kennedy could tell one voice from another, often asking after operators he hadn't spoken to for a time.

Perhaps the best-known tale of the White House switchboard involves Mary Burns, now retired, and a conversation with President Kennedy's daughter, Caroline. One December, Mrs. Burns was on the board alone when the little girl got on and asked to be connected with Santa Claus. Mrs. Burns ran down the hall and drafted a repairman to do some play-acting. Minutes later, the President called down with his thanks.

The operators stress that they never know why a call is being placed, and, of course, they never ask. They read it in the papers the next day. Often they are the last to know about a dramatic event, realizing what is going on as their switchboard, connected to the number 202-456-1414, lights up in response. The day of President Nixon's resignation they answered 102,000 calls. When the rescue mission in Iran failed, extra operators were put on duty in the middle of the night.

''The board lights up every hour on the hour, in time with the hourly newscast on the radio,'' said one operator. ''You can tell when people are listening to the news.''

The operators don't argue with irate callers, but they never put them through to the President either. ''We usually tell people the President is tied up right now but we'll take a message,'' they say. They do not accept collect calls.

Even when the White House operators fail to get their man, they do so with the panache of which legends are made. The only such case to which the operators have been known to admit occurred in the Eisenhower Administration. According to the current chief operator, who started work at the White House when Harry S. Truman was in office, the President asked to speak with Sherman Adams, then Assistant to the President, who was traveling by car in New Hampshire.

The operators found out his approximate route, contacted a nearby farmer and asked them to watch for a blue Oldsmobile with New Hampshire license plate No. 22. The farmer spotted the car and tried to flag it down, but Mr. Adams didn't stop, and didn't speak to the President until later in the day.

Illustrations: photo of Whitehouse switchboard

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