It was a day for back yard wiener roasts, a picnic with Willie Nelson in Austin, Tex., and fireworks over the Statue of Liberty.

But for hundreds of thousands of Americans yesterday, there was only one fitting place to celebrate the country's 209th birthday -- on the green lawns stretching from the Capitol to the Lincoln Memorial.

The 650,000 people who gathered there last night had to wait an extra half-hour before viewing the fireworks, the climax to the day's celebrations and traditionally its most popular draw. The delay was due to the late arrival of the Beach Boys from a concert in Philadelphia and resulted in a dual performance by the band and the 3,600 rockets and shells that formed the 30-minute fireworks display.

In the end, it was no contest: The fireworks won.

While the Beach Boys cheerfully launched into their usual crowd-pleaser, "Good Vibrations," bright white flashes lit the spectators and the ground seemed to shudder with the boom of the rockets. Cascades of red, white and blue rained from the skies, rockets zipped toward the heavens and exploded, and the crowds oohed and aahed, the music upstaged and forgotten.

"I'll take the shower in the sky over the Beach Boys any day," said Sharrain Lewis, 27, who was holding her 2-year-old daughter, Letia, in her arms as multicolored lights blossomed overhead.

Elsewhere, the Fourth was celebrated in traditional ways.

On the banks of the Charles River in Boston, about 250,000 fans listened to a Boston Pops concert. Folks rode innertubes down the Chattahoochee River in Georgia for the Second Annual Tube Parade. And, in countless cities and towns, marching bands played rousing tunes and families gathered around the outdoor grill.

At the Washington celebration, there was some grumbling about the delays -- especially among people who lost their favored viewing spots because of confusion about when the fireworks would begin -- but little real anger.

"It was worth it," said John Pennington of Fredericksburg, Va.

From the Truman balcony at the White House, President Reagan and his wife Nancy watched the display, waving to children below. The Reagans canceled their planned vacation at their California ranch because of the hostage crisis in the Middle East.

The Reagans had only to step back inside after the fireworks were over, but nearly everyone else faced a slow journey home. Pedestrians poured into the streets, further jamming the already standstill traffic; even ambulances and police cars with blasting sirens had difficulty navigating the streets.

The most serious problems were reported at the Smithsonian and Metro Center subway stations, which were mobbed as the fireworks and concert ended.

Red Cross officials said five to 10 persons were taken by ambulance from the Smithsonian station suffering from heat exhaustion. Others who fainted were simply revived by friends and continued home.

D.C. Fire Department officials said they made 200 ambulance runs to the Mall area between midnight and 1 a.m. today.

Despite such problems, the crowd on the Mall was generally well-behaved throughout the day, said Earl Kittleman, a spokesman for the National Park Service, which supervised the celebration.

Park police made about 72 arrests on disorderly conduct or drug-related charges. D.C. police made 29 arrests, mostly for vending violations.

Red Cross workers treated 1,100 people for problems caused by the heat, which reached a humid high of 88 degrees, and for a variety of other reasons. An unidentified man had a heart attack on the grounds and was taken by helicopter to the Medstar Unit at the Washington Hospital Center. A hospital spokesman confirmed the heart attack, but no other details were available.

The crowds, which covered the roughly triangular area stretching from the Capitol to the western bank of the Potomac River opposite the Lincoln Memorial and south to Gravelly Point near National Airport, represented a broad range of ages and life styles.

Young girls walked barefoot in bikinis, couples pushed strollers, and older spectators waited to see their grandchildren march by in the afternoon parade.

Under shade trees alongside the Reflecting Pool, a group of three men and women in their early thirties nonchalantly passed around a marijuana cigarette; nearby, a mounted park police officer posed while a woman took his photograph.

Two hundred yards from the performing stage, James F. Childress, a professor of biomedical ethics at the University of Virginia, was a picture of concentration as he proofread a book he is writing, entitled "The Dictionary of Christian Ethics." Around him swelled a massive crowd of boisterous, beer-drinking teen-agers.

"I can work in almost any setting," Childress said calmly. "There's something about being a part of a crowd for the Fourth of July."

As the dinner hour approached, Natalie Rowland, an administrative assistant from Old Town Alexandria, demurely sipped champagne from a crystal glass and ate gazpacho and fancy cheeses as she sat between two burly motorcycle groups.

"I'm a little up-tight with the motorcycle gangs on each side of us," Rowland said. "I'm a little up-tight with all kinds of people in various stages of drunkenness.

"But where else can you go to see such a human tapestry? One only has to think of the hostages to appreciate this kind of freedom."

For the most part, the 39 rescued hostages of TWA Flight 847, who returned to the United States earlier this week, spent the holiday quietly with family and friends.

Former hostages George Lazansky and his wife Joann of Alonquin, Ill., passed the day at Wrigley Field in Chicago, where Lazansky tossed out the first ball in the game between the Cubs and the Giants, at the Cubs' request.

For some revelers in Washington, the day began extremely early.

At 2 a.m. yesterday, 500 people were already milling around the Washington Monument -- the hardy souls who had staked out the choicest seat close to the stage.

One small group was playing touch football in the light of a full moon. Some were sprawled out, somehow able to find sleep despite the din of music from dozens of radios and cassette players and the frequent blasts of firecrackers.

Jim Burke, a 37-year-old computer operator and Vietnam veteran, said he drove from Houston with his 15-year-old daughter to see the Vietnam Memorial and take part in the festivities. They camped out on the grass with sleeping bags and ate cold cuts and French bread.

Another young woman and her husband, sprawled on a sleeping bag and smoking marijuana, had begun hitchhiking Tuesday evening in North Carolina.

She said she was a construction worker who worked nights as a saleswoman in a tattoo parlor. Her arms were covered with tattoos of lions, serpents and other animals.

"Things are really mellow right now," she said. "But it's going to be a real madhouse . . . . There was nowhere better to go, really."

Once groups had staked out a certain piece of territory on the Mall, they guarded it jealously.

Susie Morin, 18, of Kensington, and her friends Meg Smith, 19, of Philadelphia, and Molly Garcia, 19, of Rockville, drove stakes into the ground to rope off their own piece of the Mall.

"Excuse me, you're trespassing," Morin said to a man who stepped within the boundaries.

While Frisbees whizzed by them and waders splashed in the Reflecting Pool, Johanna Gahtan of Inglewood, N.J., her son, Raymond, and daughter, Vivian, were a tranquil trio, each engrossed in a paperback.

Garlan Black and his wife Delilah, vacationing from Nashville, sat on a bench and engaged in an interesting session of people-watching.

"We just saw a man walk by in a plaid skirt," said Garlan Black, 55, an electronics supervisor. "Delilah said, 'Maybe he's Scottish,' but I don't think so."

The Blacks were also fascinated by a group of about 50 teen-agers in stiffly spiked Mohawk haircuts, black motorcycle boots and chains, who gathered under a nearby tree. "I don't believe I saw them in Tennessee," said Black.

The group members, who identified themselves as "resident punks and visiting punks," said they were drawn to the Mall with a patriotic spirit and an entrepreneurial one.

"It's our free country, too, you know," said Brian Samuels, 17, of Arlington, dressed all in black.

"They want to take our pictures, but they have to pay," said a 16-year-old who identified himself only as "Dave." Dave, whose jet-black hair rose in stiletto spikes, wore plaid pants and a white T-shirt and held a dripping popsicle in one hand and a beer in the other. "We charge them $1 or $2." By midafternoon, the group had earned only enough for ice cream, about $3.

On nearby Constitution Avenue, school bands from Beaver Dam, Wis., Dadeville, Ala., and Minot, N.D., paraded by.

Richard Pohl of Minneapolis took in the fresh-faced youngsters in the band and the partying, sunning, picnicking throngs around him and said, "I think it's great. I was just thinking: What would this parade be like if it were in the Soviet Union?

"You don't have tanks lined up. You've got bands from Topeka, Kansas. The thing we're celebrating is the American people."