President Carter, who learned some expensive early lessons about campaigning against an incumbent president in 1976, is applying those lessons this year as he watches Ronald Reagan go through some of the agony he suffered four years ago.

Carter has begun his campaign for reelection in the classic fashion of the incumbent, judiciously selecting a limited number of campaign appearances but never straying too long from Washington and the advantages of the White House.

In an era when campaigning for president often revolves around television's evening news, Carter can "make news" simply by going about his job, appearing as the hard working chief executive while still getting across his political message.

Yesterday, for example, reporters at the White House were invited to witness the signing of a new military manpower bill, which was another opportunity for the president to reiterate his commitment to a strong defense as he and Reagan jockey for the title of the country's most pro-military politician.

For Reagan, it is far different. Although the Republican nominee has started his campaign in a less frenetic manner than Carter did four years ago, he has to campaign more than the incumbent just to get his share of attention. And, according to a Carter aide who was reflecting on the lessons of 1976, "the more traveling you do, the more chance there is to make mistakes."

Last month, during the Democratic National Convention, Carter's pollster, Patrick Caddell, argued that when it comes to running a general election campaign for president, there is no substitute for experience. If the GOP nominee thought that this fall would be like any of his other campaigns, Caddell said, "I've got news for Ronald Reagan."

The difference, according to Caddell and others who have been through the experience and who intend to put that experience to good use this fall, is the intense scrutiny a presidential candidate is subjected to and the extent to which mistakes on the campaign trail tend to be magnified.

Recalling 1976, White House press secretary Jody Powell said, "You learn not to try to do 12 things a day because invariably something will go wrong with one of them and that is what people focus on . . . The mistakes will step all over everything else you do."

The president made no mistakes of the kind that have plagued Reagan as he began his campaign last week. While, in the words of one White House official, "we still have a long way to go," the first week clearly boosted the confidence of Carter aides that they can overtake Reagan by Election Day.

According to Powell, the president intends to conduct an active, free-wheeling campaign that will be deliberately structured to contrast with what he call the "tightly controlled" Reagan operation.

To reinforce that impression, Carter was on the road for the first three days of last week -- at the Labor Day picnic in Tuscumbia, Ala., at a "town meeting" on Tuesday in Independence, Mo., and at the Italian market and a black Baptist Church on Wednesday in Philadelphia.

Thus, the evening television news for much of the week showed the president out campaigning actively, as promised. But it was not the Jimmy Carter of 1976, wildly careening around the country, but the president of 1980 running his own tightly controlled road show.

Moving at a leisurely place, Carter had a single, central event in each of the three cities he visited and generally succeeded in getting his message across without the kind of distractions that have bothered Reagan.

The president allowed reporters traveling with him to question him only once during the three days -- in Independece on Tuesday, the day after Reagan had erroneously labeled Tuscumbia, where Carter kicked off his campaign, as the bithplace of the Ku Klux Klan.

Wrapping himself simultaneously in the American and Confederate flags, the president said he resented his opponent's "slur" on an entire region of the country and his attempt to divide the South from the rest of the nation.

Shortly thereafter, Carter also demonstrated his mastery of the "town meeting" device he has used so successfully. He turned one critical question on his policy of increasing defense spending into an attack on Reagan as a potentially dangerous cheif executive who might get the country into war.

Reagan, Carter charged, intends ato initiate "a massive nuclear arms race against the Soviet Union" that would jeopardize world peace.In response to another question, he suggested that Reagan does not "believe in peace."

The issue of peace and the suggestion that Reagan would threaten peace was a central theme of the president's first campaign week as his attempt to portray his Republican opponent as a warmonger lost the little subtlety it had in the first place.

Carter strategists insist that they are not counting on Reagan to continue stumbling. "I'm sure they'll get their act together," one official said.

But they also believe that Reagan has already damaged himself, raising questions about his fitness to be president and speeding the return of dissident Democrats unhappy with Carter back to the party fold.

For a while, at least, the president is unlikely to allow Reagan as much room as possible to make additional mistakes and raise new questions out on the campaign trail by himself. After the initial flurry, Carter is scheduled to make only one campaign appearance this week, in New Jersey.