President Carter and Ronald Reagan meet in Cleveland tonight for the long-awaited debate that could be the crucial event in determining who will be the next president of the United States.

Their clash comes on the heels of a Gallup Poll report yesterday that voters have swung sharply toward Carter in the last two weeks -- a six-point shift that now gives the president a three-point lead over his Republican challenger.

With the crucial debate just hours away, the president put in a day of political business as usual yesterday, with a campaign stop in West Virginia, before flying to Cleveland last night. Reagan spent the day at his rented Virginia estate, meeting with former president Gerald R. Ford and being drilled for the event by his top advisers.

Meanwhile, the League of Women Voters announced the four journalists who will question Carter and Reagan in tonight's 90-minute debate, which is scheduled to begin at 9:30 p.m. EST. The panelists are Marvin Stone, editor of U.S. News & World Report; William Hilliard, assistant managing editor of the Portland Oregonian; Harry Ellis, economic and energy correspondent and deputy Washington bureau chief of the Christian Science Monitor, and Barbara Walters of ABC. Howard K. Smith will serve as moderator.

Carter now leads Reagan 45 to 42 percent, according to the Gallup Poll released yesterday. Independent John Anderson now has 9 percent, with 5 percent undecided. The poll has a margin of error of 4 percentage points, which means that the race is essentially even, according to the Gallup figures.

Two weeks ago, in polling done between Oct. 10 and 12, Gallup showed Reagan ahead of Carter by 45 to 42 percent, with Anderson at 8 percent and 5 percent undecided. The most recent Gallup Poll was conducted from Oct. 24 to 26, and was based on a sample of 1,100 registered voters (of whom 800 were classified as likely voters).

The poll shows that Carter has succeeded to considerable degree in raising doubts about Reagan's ability to keep the nation out of war, and that Carter is now benefiting from an increase in the public's confidence in his ability to deal with the Economy.

In contrast to the Gallup figures, the Louis Harris Survey done for ABC News showed no appreciable change in the past two weeks. The figures showed Reagan maintaining a three-point lead over Carter, with 45 percent compared to the president's 42 percent, while Anderson had 10 percent. Two weeks ago, the Harris figures showed Reagan 42, Carter 39, Anderson 12. The Harris Survey has a 3 percentage-point margin of error, which means that the race is actually about even by his calculations.

According to Andrew Kobut, an official with the Gallup Poll, foreign policy has played a decive role in the campaign so far. Carter began to make progress in the polling results after the outbreak of the Iran-Iraq war, he said That is when public confidence in Carter's handling of foreign policy issues began to soar.

In tonight's debate, Reagan is faced with a crucial, dual battle requirement. He must take to the offensive, in trying -- more effectively than he has in the past -- to focus national attention anew on the Carter economic record. But at the same time, he must concentrate on his own defense, in order to calm nationwide concerns that have stemmed from his long record of hard-line pronoucements on the use of U.S. military force around the world.

Reagan's strategists, realizing the importance of the debate, cut back Reagan's schedule last week in order for the candidate to remain at his rented estate, Wexford, in Virginia since last Friday. The Republican standard-bearer has immersed himself in debate preparation since then. He planned to fly to Cleveland this afternoon.

At his home, Reagan's advisers helped the candidate prepare by firing sample questions his way. Emphasis was on issues of foreign policy and the economy. Reagan also had lunch at his estate with Ford, the last Republican who met Carter in a presidential debate. Ford said he told Reagan to anticipate some show of Carter "meanness." He also told reporters that if Reagan is perceived as the winner, "that will insure his election."

After Reagan canceled a scheduled Sunday taping of an interview for the ABC show "Good Morning America," his press secretary, Lyn Nofziger, explained: "We're not going to do anything between now and the debate except prepare for it."

The format for tonight's debate is this: There will be an initial 40-minute section in which each panelist directs a question to one candidate and then directs the same question to the other candidate. Each panelist will get one follow-up question, and the candidates will also get a brief rebutal.

In the second segment, also 40 minutes long, each panelist will ask a second question. No follow-up questions will be allowed, but the candidates will be able to offer a rebutal, followed by a surrebuttal.

Finally, the two candidates will make closing statements.

All of the panelists and moderator Smith planned to attend a working dinner in Cleveland last night, where they were to be briefed on procedures by the league. They then planned to discuss the questions they intend to ask.

According to a spokesman for the league, the panel's selection was made on criteria that stressed diversity: the league wanted a woman and a black, plus a geographical distribution and a division that included magazine and newspaper and television representatives.