Sen. Ernest F. (Fritz) Hollings of South Carolina formally entered the race for the Democratic presidential nomination today with a rebuke to his own party--as well as to President Reagan--for mismanaging the economy.

Hollings charged in his announcement speech here and again in Washington that Reagan is "putting America out of business" with disastrous federal budget deficits and shortsighted policies. But he warned that the Democrats must have a candidate who can restore fiscal discipline if they hope to win back the White House.

"The Democratic Party lost the 1980 election because we lost the faith of the American people," the senator declared. "Every time a special interest appeared, we responded. And every time a problem arose, we had but a single solution: spend more money."

Hollings, who advocates a virtual freeze on federal spending increases, said such austerity would hurt but argued that it is vital.

"For generations," he said, "Democrats managed the economy responsibly. We will not be returned to the White House until we prove we can do this again."

A former governor of South Carolina, from 1959 to 1963, and once chairman of the Senate Budget Committee, the silver-haired Hollings, 61, announced his candidacy as an admitted long shot, complete with brochures describing him as "The Thinking Man's Dark Horse for 1984." But he said he felt he had plenty of time to catch up with the front-runners, whom he described as far less experienced in matters that count.

Right now, said John Patterson, publicity director for the Hollings campaign, "his worst problem is recognition. We don't have to build his image. We have to expose it."

An outspoken iconoclast with a thick Charleston drawl and folksy style, Hollings formally announced his candidacy on the airport campus of Midlands Technical College here. The school was established when he was governor and Hollings said he chose the site to illustrate the need for new jobs and his credentials in helping create them.

By contrast, Hollings contended later on a flight to Washington for a luncheon at the National Press Club, the other Democratic contenders were neophytes.

He said that former vice president Walter F. Mondale "was an attorney general in Minnesota , an appointee. He never created a job."

" Sen. John Glenn a former astronaut was training for a job. Sen. Alan Cranston still doesn't understand what we're talking about. And Sen. Gary Hart thinks it's a new idea. We were pulling ourselves up by the bootstraps in South Carolina 20 years ago."

Hollings saved his sharpest barbs for President Reagan, however, whom he assailed as the biggest spender of all, a man who "has delivered us disastrous deficits, caused Depression-level joblessness, and . . . demolished the consensus we needed for the rebuilding of our depleted defenses."

Reagan's deficits, Hollings said, are adding $1 trillion to the national debt over a five-year period and are costing $100 billion a year in interest. The South Carolina Democrat said his spending freeze would save $700 billion over five years and "restore fiscal integrity to government, investment incentives to industry, and jobs to the unemployed."

Hollings also criticized Reagan, and his predecessors as well, for going along with the State Department and "always representing the other government" in disputes over international trade practices.

More and more, Hollings said, foreign governments are active partners with business and labor in their countries, while here in the United States, President Reagan "rests on the dangerous and debilitating delusion that government is the enemy."

"With this ideology, Ronald Reagan is putting America out of business," Hollings charged.

In his fourth term in the Senate, Hollings, who stands 6 feet 2, keeps trim by playing tennis most mornings, jogging when it rains. He has been testing his candidacy in 44 states over the past year, often traveling with his second wife, Peatsy, who sometimes stands in for him giving speeches.

Hollings acknowledges that he has to "to get over the hurdle of the Carter presidency" and establish himself as a different kind of southerner. But he notes that "the other Fritz Mondale has that hurdle, too."

For the moment, nothing seems to exasperate Hollings more than what he regards as the media's preoccupation with such questions as how much money he's raised ($450,000 so far) and how big his campaign staff is (24 full timers) instead of focusing on what he has to say. He also said he is not at all interested in becoming vice president.

But he agreed that he has to seem to be shedding his dark-horse image by next January. Holllings is banking heavily on the New Hampshire primary set for March 6 for the chance to make a strong showing and establish his "centrist" candidacy as a credible one.

"In New Hampshire," he told reporters this morning, "we've got to be right at or near the top." If he doesn't finish close behind Mondale there, Hollings said, "I'm going to be in trouble.