TO MAKE the White House a home isn't easy.

The State Dining Room is not the sort of place for pizza nor the Blue Room a place for lounging around. Yet after all the prime ministers and princes depart, the president is entitled to take off his shoes and read his book. And the first children have the right to put on their jeansland put up their feet.

Ensuring the domestic tranquility in the White House is one of the first lady's jobs. Rosalynn Carter has taken up and solved the problem of where the president can read after supper. Now she's gone on to redecorate the third-floor solarium and its adjacent game room for the Carter children. And she still has other plans for the White House.

Everything she's done to the White House to date seems at peace with the laid-back, less-pompous style the Carters have brought to the White House -- picnics on the South Lawn, classical music in the East Room, wine instead of whiskey, place settings of contemporary American glass and pottery at a luncheon for Senate wives and American impressionist paintings in the family quarters.

Mrs. Carter's White House is very much in the Southern tradition. Like most Southerners she is proud of her heritage of hospitality. There is a softness about the best of the Southern style, and this softness she brings to everything she does at the White House. This softness, by the way, is only in manner. Like the traditional Melanies of the South, Mrs. Carter seems to be a sturdy, strong woman who's not to be trifled with. Northerners frequently mistake the soft-spoken Southern accent, the quiet manner, the "after you, please" for lack of purpose. But Southern women of Mrs. Carter's generation were brought up to make decisions, push people into positions, get things done behind the scenes -- all with an air of "Who me? This little old thing?"

It is also a tenet of the Southern style, that while you must always put your best foot forward -- no part of the country loves antiques, silver or porcelain more -- you must always avoid any sense of being "uppity" or "of putting on the dog." Even though you've spent the last three days cooking dinner, you try to give the impression you whipped it up innothing flat. The aim is to be elegant, but put your guests at ease.

So that's what Mrs. Carter is doing at the White House. She started with taking care of the State rooms by heading a discreet campaign organized by curator Clement Conger to raise a $10-million endowment for White House furnishings. Now she's gone on to making the family quarters comfortable.

On a recent afternoon after her Spanish class, while waiting for Amy to come home from school, Mrs. Carter gave a rare glimpse of what it's like to live over the store, in the most-visited home in the world.

Mrs. Carter came into the solarium a bit anxiously. "I'm not sure how straight it is. I didn't have time to check," she said. The room was, of course, in apple-pie order. But Mrs. Carter, who is a woman who notices and cares about small housekeeping details, was annoyed to find a bulb burned out in the hall. And she was really unhappy when she saw someone had plopped a Ping-Pong table top over the pool table without removing the pool table cover.

Mrs. Carter, one gathers, didn't find the house and its 100-odd rooms intimidating -- she has too much poise for that, not to mention her experience in running the Georgia Governor's Mansion, a good apprenticeship. She said the White House antique collection, for example, was a "post-graduate course for me, because we had a major collection of antiques in the Governor's Mansion in Atlanta."

Mrs. Carter likes to tell about the time her husband was an administrative officer in the Navy. He ordered an art course for a sailor, who transferred before the course came. So the Carters took the course, learning the rudiments of drawing, painting and art history. That was the beginning, Mrs. Carter said, of their interest in art -- and another example of the Carters' habit of never missing a chance.

Mrs. Carter said she has always felt at ease in the White House. After all those years of campaigning, "my family had been mobile for so long, in all directions, that when we were finally together here in the White House, and could unpack, it was home."

The first year or so the Carters were in the White House, she said, "We didn't change anything." In the last few months, though, she's begun to settle in rather like someone who is planning to be around, say, six more years or so. Funds for the changes all came out of the money Congress appropriates to maintain the White House.

The State rooms are on the first floor; these are the ones the tourists see. At night, this is the gala floor, where under enormous glittering and jingling crystal chandeliers, politicians and potentates, emperors and entertainers meet, greet and eat.

The second floor is divided into the Lincoln and Queen's bedrooms with sitting rooms at the east end and the president's suite, dining room, kitchenette and family bedrooms at the west end.

The third floor has two suites, two guest rooms, ironing and laundry rooms, servants' changing rooms and the billiard room. Up a ramp to the flat roof is the solarium. On the other side of the roof is a greenhouse.

First on Mrs. Carter's agenda was the problem of where to sit comfortably and relax after dinner. Cozy, comfortable and warm places aren't plentiful in the White House -- especially, Mrs. Carter pointed out, "since we keep the thermostats turned down." She said that after dinner is about the only time the president has to relax. He likes to "watch the television news and then read."

The second floor has one of the most beautiful parlors in the White House, the Yellow Oval Room. The ladies retire here, after intimate dinner in the President's Dining Room on the second floor. The Carters recently have given a number of these small dinners, for the press and for old friends and supporters. Such an invitation for conversation instead of ceremony is counted by many as the ultimate compliment.

The Yellow Oval Room is carefully furnished with splendid antiques of the early Federal style. But White House Curator Clement Conger, according to reports from more than one administration, is much more interested in 19th-century authenticity than 20th-century comfort. It's the sort of room you might feel out of place in unless you have on a long skirt (preferably hooped) or a powdered wig and knee breeches.

The West Sitting Room at one end of the second floor isn't all that comfortable, either. It's really only one end of the cross hall, a long narrow corridor repeated on every floor of the White House. Many doors open into it -- for one, the president's study (used by President Nixon as his bedroom) and the connecting bedroom. As did the Fords, the Carters share bed and bedroom. The President's Dining Room opens into the sitting room from the other side.

First Mrs. Carter moved two chairs into the dining room in front of the fire-place, but that didn't work. A month or two ago, she finally solved the problem by having two comfortable chairs, friendly fashion, sharing a single ottoman, put in the president's study. "Jimmy never worked there," said Mrs. Carter. "And it has a fireplace." So that's settled.

Mrs. Carter's biggest project so far has been the solarium, the family room of the White House. This is the area Grace Coolidge called the "sky room." In Lincoln's day, this whole area was the attic, where Todd Lincoln and friends played. During the Kennedy administration, Caroline and friends had nursery school here. Various presidential children entertained their dates in the room.

Sons Jeff and Chip Carter, Jeff's wife Annette, and, until their recent separation, Chip's wife Caron and son James, use the room now as their living room. It is handy to their three- or four-room suites on the third floor.

The solarium is about 20 by 35 feet, an octagon (a handsome shape), with wide, deep windows facing south. A white balustrade encircles the roof. It's a passive solar energy room -- one of President Carter's concerns.

"Isn't the view wonderful?" Mrs. Carter asked. Above the balustrade, one can see the Washington Monument and the Potomac River. "The White House staff keeps the flower boxes planted with the season, tulips and now evergreens."

"We stay here so much," she said. "The children the most.We come up here on Saturdays and Sunday afternoons. Sometimes Jimmy and I eat up here. But not much. The children eat here when we have guests on the second floor."

"Did you see the kitchen?" Mrs. Carter asked. "We put in the tiles.It used to be yellow, too." The kitchenette, hardly bigger than a closet, is tucked off the solarium. The tiles are Portuguese scenic designs in colors from the main room.

Mrs. Carter said she likes to cook. "But I haven't had much chance to cook in years. When Jimmy was governor, I used to go to cooking classes, taught by Ursula Knaeusel, just to keep my hand in. We would all cook her recipes and then get to eat it all up. I found the cooking classes very relaxing." Now, she said, "The staff leaves after lunch on Sundays and I cook a bit then. Though most of the time they leave enough in the refrigerator for us."

Mrs. Carter invited her guests out on the quarry-tiled roof, on a level with the solarium, to see where her grandson James sunned in his playpen when he lived at the White House. "Around on the other side," Mrs. Carter said, "there's a greenhouse. Jeff is interested in growing things."

Jeff also has a telescope. "We look at the stars up here. You'd be amazed at what you see. Ducks, for instance. We didn't know what they were at first. All silvery underneath."

Twice a week, Mrs. Carter and daughter-in-law Annette take Spanish lessons in the solarium. This is also the place where Mrs. Carter had her State Department briefings for her Latin American trip. She said she'd do better in Spanish, she thinks, "if I could practice more or had someone to talk with. I don't understand everything. But I can get along."

She enjoys it, she said, because "it's kind of an escape for me... from the pressures... the things you have to do, the mail and everything that comes in. I know at night, Jimmy likes to go down to see a movie, because he can escape from it all and rest. Spanish is the same way for me. It's an escape from what you have to do.It's something I enjoy.

"I don't think the third floor had really been used much in a long time," said Mrs. Carter. Wayne Dean, the interior designer from Americus, Ga., who worked, with Mrs. Carter on the room, was blunter. "It would be too kind to call it awful. The curtains and the furniture were covered in a horrid polka-dot chintz with weird tangerine-colored flowers," he said later by phone.

Now the room has a pleasant, sunny contemporary feeling to it. The ceiling and walls are a pleasant off-white, instead of the brilliant yellow it once was. A pair of soft sofas have been re-covered with a subdued blue, white and yellow stripe. The two easy chairs are now in a cloud pattern. The geometric rug is in the same colors. "We didn't buy a lot of things," Mrs. Carter said.

Annette Carter, who has a degree in interior design, was a big help in major decisions on the room, Mrs. Carter said. "Wayne would bring us samples and Annette and I would go over them."

Mrs. Carter gave the grand tour of the family pictures on the wall of the game room. The pictures are revealing because they show the events and the people the family likes to remember.

By the entrance is a picture of Adm. Hyman Rickover and President Carter, standing face to face. Jason, the son of the Carter's son Jack and his wife, Judy, is pictured in a velvet suit his grand-father once wore. "Jack and Judy are expecting another baby in a couple of weeks," Mrs. Carter said. There also are pictures of Mrs. Carter's sister and mother, of the president when he was in the Navy, of the Carters walking down Pennsylvania Avenue after the inauguration, of Miss Lillian and Hubert Humphrey together. One shows the president at his inauguration, another a year after at an Atlanta fund-raiser. "They said he looked tired," said Mrs. Carter. "I thought he looked great.

"Jimmy likes to take pictures. He used to develop his own. When Annette did her thesis for her interior decoration degree at the University of Georgia, on the Chinese porcelain collection in the Governor's Mansion, Jimmy took the pictures for her," Mrs. Carter said.

Jeff is a very serious photographer. There was talk once of him doing a book of White House photographs. Even Amy has taken a photography course at school. Framed on the walls is a picture of the White House by Amy. "It was the first she took, and I think the best," Mrs. Carter said, and laughed.

Then Amy came home from school bringing a Christmas catalogue that she was reading. She set up the chessmen for her mother, correcting her mother as she went. "I don't play chess," said Mrs. Carter, "but Amy does."

Mrs. Carter said Amy once said she'd seen Lincoln's ghost, but Amy denied it this day. In the matter of the secret stair-cases, Amy turned out to be the expert. Not only did she know about the one her mother did, which goes from the second floor to the third ("you just push a panel of the wall in," Mrs. Carter explained), but she also knew of another that begins in the kitchen and goes all the way up to the top floor. Amy was not very explicit about just where it is. Secret staircases need to be secret.

Not long after, Amy and her mother rode the elevator down to the second floor -- where Amy went to do her home-work and her mother to return the president's call. It may be the White House to you, but it's home to the Carters.

The see-through lucite and glass table, a 54-inch octagon like the room, is the most important piece of furniture. "After we put the table in here, Jerry Rafshoon's wife, Eden, came in and recognized it. She'd designed it. We didn't know'til then." Lucite brackets also hold white pots of ferns.

Six imported Spanish chairs, hand earved in what Dean calls a "sophisticated primitive" manner, are painted blue with a gray glaze over them. The lamps are in the Chinoise style, American white porcelain. The coffee tables are brass with copper studs.

"This was made in the carpenter's shop, here at the White House," Mrs. Carter said, pointing to a large white eabinet. "It holds the television and the stereo, that sort of thing."

Two tracks of movable lights go down each side of the room. "It was hard to find a place to put them in, because there's no crawl space in the ceiling. It's a major task to do anything electrical," Dean said later. He thought the lights should stay high because "the ceilings aren't that high, just about nine feet."

Mrs. Carter pointed to a small sprightly statue of a horse. "I bought it in Nigeria," she said. "What Amy likes to do is shop. You know when King Hassan was here, they were going to take the prince to the zoo and to the Air and Space Museum. I asked him afterward, 'How did you like the zoo,' and he said, 'I didn't go.' And I asked him 'How did you like Air and Space' and he said, 'I didn't go.' It turned out he had spent the whole day shopping. Amy's like that."

Moving out into the hallway, down the ramp to the third floor, Mrs. Carter pointed out the pictures on the walls. "When we came here, there wasn't anything on the walls. They were just painted white with a red runner." The pictures were selected by the curator's office. The historic group includes a submission for the Capitol design competition and a drawing of George Washington. All are hung upon a blue wallpaper, a Chinese tea chest design.

Mrs. Carter showed a small sitting room at one end of the third-floor book-lined hall. The room has a double stair-case leading up to the roof. "It's a place to go when you need a bit of privacy," she said. Annette Carter has filled the cases here with pretty things from their travels, including an Indonesian carving.

Off the third floor hall is the game room, a popular place with the family. It once was painted all green -- "telephone truck green," Dean called it. An air conditioner was stuck in the window. Now there are shutters, painted blue, and grasscloth wall covering. Bamboo chairs, once painted yellow and used in the selarium, have been stripped of paint and now serve as bleachers.Over the pool table is a modern version of the pool-hall lamp, designed by Dean.

Jeff Carter, who turned up when his mother had to go downstairs briefly to receive a delegation, said the Carters all play Ping-Pong, "but Dad's the best." To the question of how long it took him to feel comfortable at the White House, he answered, "I feel comfortable wherever I am."