Jimmy Carter, the son of the rual South who ran in part against the problems of big government, gets his chance today to grapple with the realities of national governance. He becomes President of the United States in a frigid capital glistening with ice and awaiting Carter's call to a new era in American life.

When Carter raises his hand to take the oath of office on the inaugural stands below the Capitol dome, a tumultuous period passes into history. His inauguration returns the Democrats to power after eight years, ends divided party rule between Congress and the White House, finally puts behind us the Vietnam-Watergate years, and gives Americans again an elected President and Vice President.

The inaugural oath is scheduled to be administered at 12 noon on the traditional presidential pavilion constructed over the east front steps of the Capitol. Television networks will carry the ceremonies live beginning at 10 a.m. People around the world also will witness, through satellite transmission, the most solemn ceremony in the American experience.

Today's inauguration is the nation's 48th. Jimmy Carter, of Plains, Ga., becomes the 39th President and the 38th person to serve in that office (Grover Cleveland served two interrupted terms. His assumption of power closes another long and bitter historical gap.

It's been 125 years since a politician came out of the Deep South to become President. Jimmy Carter, a man of many parts - peanut farmer, naval officer, businessman, governor among them - won his victory last November with the solid support of the Old Confederate states. But his selection could not have been achieved without the massive backing of blacks across the South.

That sense of something new, of a break with the political past, permeated Washington on this inaugural day.

Washington itself reflected the spirit. For days the tempo of city life has been rising. Streets are clogged with traffic, hotel lobbies are jammed, train and air terminals unusually busy.

Jimmy Carter has promised a "people's inaugural," and indeed many firsts accompany this celebration. One of the most symbolic takes place several hours before the swearing-in.

Martin Luther King Sr., the old Baptist preacher from Atlanta, is scheduled to begin the official inaugural day events with a poignant reminder of past and present. He returns to the steps of the Lincoln Memorial, where his late son led a nonviolent army of blacks and whites in that memorable march on Washington more than 13 years ago, to lead a prayer service.

Everyone is invited to participate and hear Dr. King preach the sermon - everyone, that is, bold enough to face the below-freezing temperatures predicted for the 8 a.m. service.

Actually conducting the service will be the Rev. Bruce Edwards, pastor of the Baptist church in Plains where Jimmy Carter regularly teaches Sun- day school. Only last Sunday Carter bade farewell to the parishioners in that church in an emotional scene.

Yesterday, before coming to the capital he had campaigned so long to govern, Carter said a last good-bye to the citizens of his small hometown. He went to the train depot to greet some 375 people leaving on a special train to Washington. That's almost half the entire population of Plains, Ga.

Carter was in an ebullient mood. He shook hands, slapped backs, joked with old friends, and said:

"It's going to be a new day, a new beginning, a new spirit for your country. I will try to do a good job for you."

He offered a last piece of advice, in humorous vein. "If you get into trouble, don't call me," he said.

Carter returned to his home, now cordoned off by Secret Service agents, watchtowers, guard gates, and lights - the symptoms of the isolation of the office that he already has complained about publicly. He then locked the front door, carried his suit bag to a waiting limousine and left to fly to Washington.

He got to the capital long before his fellow townspeople were due to arrive on that special train. His arrival came one year to the day after he won his first campaign victory, the Iowa Democratic Party State Caucus. That triumph propelled him along the road to the White House through a long and exhausting campaign year.

Inevitably, this is Jimmy Carter's day: the focus is on the future. But it's also the day when power - and problems - end for Gerald R. Ford.

Four years ago Ford was only oen more congressional face in the crowd at the Capitol. He was watching as Richard Nixon and Spiro Agnew took their second oath of office after winning one of the greatest presidential victories.

Within two years both Nixon and Agnew had resigned and the presidency faced its most severe test. Both Ford and Nelson Rockefeller, whom he later appointed as our second unelected Vice President - Ford was the first - are scheduled to leave Washington today about the same time, 12:30 p.m., from the same airport, Andrews.

Ford and his wife, Betty, are heading for California, Rockefeller and his wife, Happy, for New York.

All presidential inaugurations are a mixture of serious ceremony and pageantry. Carter's is no exception. But few, in recent years anyway, have been so dominated by a desire to accommodate the public.

Free bus service from city and suburbs is planned. Two hours of free rides on Washington's new subway system are also being offered to all. Another innovation in the name of the citizen observers will be seen along the inaugural parade. There will be no bleachers along most of that 1 1/2-mile passage between Capitol Hill and the White House. People this year will not have to buy tickets to watch the President and the parade passby.

Carter plans another break with tradition. He plans to get out of his limousine and walk the last two blocks to his solar'warmed reviewing stand in front of the White House. Then he will atach the parade in his honor pass in review.

The parade is supposed to begin at 1:30 p.m. and last one hour and a half. Most of the statistics are familiar: 15,000 people participating, 54 bands, 31 floats, 17 equestrian units, six horse-drawn vehicles. There will be, in keeping with the spirit of the day, a giant peanut-shaped balloon. Acting as parade marshal is Sen. Hubert H. Humphrey, so long a leader of the Democratic Party and now recuperating from a major operation for cancer.

As in the past, the inaugural events represent weeks of planning and a maze of problems to confront. Soldiers will be standing on guard to battle snow; they've already been hacking away at the ice on Pennsylvania Avenue for several days. Arrangements for medical teams, portable toilets (eight federal buildings will also be open for toilet facilities), vendors of hot dogs and coffee teams to assist the handicapped - all are in readiness.

"People's Inaugural" notwithstanding, not everything on this day is public. In this inauguration celebration, as in all others, some people are more equal than others. There lie many of the problems connected with putting on this $3 million party.

Only 55,000 people can get into the seven official inaugural parties being held tonight. You had to be invited to buy a ticket. Hundreds - perhaps thousands - of Carter workers and supporters across the country are insulted because they were not invited to the parties, or, to buy one of the 19,000 parade seats which also cost $25 apiece.

The 300,000 general invitations Carter asked the inaugural committee to send out were also confusing. People are arriving in Washington thinking that the large beautiful invitation entitles them to get into everything. It doesn't. It's a souvenir.

And, naturally, others were upset. Leaders of the Jewish and Orthodox Christian communities are pointing out that for the first time in 20 years only Protestant and Catholic clergy have been invited to offer prayers at the Capitol ceremonies. A Jewish cantor is scheduled to sing the National Anthem at the end.

But in terms of history, those are insignificant concerns. What will be remembered of this day is that a relatively obscure politician from the rural South, running against all the odds and all the prognostications of the political experts, decided he had a chance for the presidency. He was telling everyone he met two years ago he was going to be the next President. Few, if any, believed him.

Today, he enters the White House.