After 10 months in office, President Reagan shows no sign of succumbing to the temptations of the imperial presidency.

More than any other recent president, Reagan likes to tell a joke at his own expense, and he even turns aside with good humor criticisms that go to the core of his presidential style.

How closely Reagan follows daily developments, how engaged he is in the process of governing and how he arrives at decisions are questions that often remain mysterious to outsiders late in the first year of Reagan's presidency.

The president is well aware of--and reportedly not pleased by--a trickle of articles that describe him as somewhat disengaged from the business of the nation, but his public response is the joke, not the retort.

A recent example came in Reagan's ABC interview taped Tuesday. Reagan had just flown to California after ordering a temporary halt to nonessential government work during Monday's budget confrontation with the Congress.

He made a joke when asked whether he had classified himself as an essential worker. "No one told me whether I was or not," the president replied. "I sat there in the office just in case somebody tried to take it over."

It is hard to imagine other recent presidents even cracking a smile over such a question.

But while Reagan's approach is far removed from the imperial manner of a president who invokes his authority at every moment and reacts sharply to all perceived slights, his style does create some puzzlement.

At times the president is clearly very well informed. In a March interview, for example, he answered without hesitation questions on African policy that were far from the forefront of his concerns at the moment.

On other occasions, Reagan leaves the impression that he has only a hazy understanding of a complicated issue.

On Oct. 2, for example, the president appeared in the White House East Room with Defense Secretary Caspar W. Weinberger to announce his decision on deployment of the MX missile and construction of the B1 bomber. Reagan agreed to answer a few questions before turning the microphone over to Weinberger, but he appeared distinctly uncomfortable and unprepared.

Some of his press conference performances have been relaxed and impressive. Others have stirred a new round of questions about how closely he is in touch with events.

In his initial round of meetings with foreign leaders, Reagan has done better than some critics had suggested he would. He has had many more successes than problems.

Weinberger said recently that every foreign head of state has come away from a first meeting with Reagan very impressed and holding "a revised opinion of Reagan's strength as a leader." The score may not be quite so perfect, but the president has served his policy purposes well in most of his top-level encounters.

One part of the Reagan puzzle is that he often is showcased dealing with the lighter side of his life as president.

This week, for example, he gave two interviews, both heavily devoted to his life on his mountaintop ranch here.

When he talked with a New York Times reporter, the ground rules were that only questions about the ranch could be asked.

With Barbara Walters, he took questions on some major issues, but the bulk of the hour-long program was on the ranch and Reagan's personal life, including his relations with his parents and children.

Presidential counselor Edwin Meese III, chief of staff James A. Baker III and Weinberger were making themselves available for television interviews about the budget showdown with Congress and forthcoming weapons talks with the Soviets while Reagan gave his lighter interviews.

The contrast was underlined when Walters asked what had been the toughest decision of his presidency and he replied, "It could have been the veto of the continuing resolution to fund the government the other night."

It would be interesting to hear the president explain why he considers that confrontation, which he called "a game of chicken," a harder decision than his budget-cutting decisions, the decision to sell AWACS aircraft to Saudi Arabia, deployment of the MX missile or his message to the Soviets on arms reduction in Europe.

The decision-making procedure in the Reagan White House adds to outsiders' puzzlement over the president's role.

In essence, Reagan is presented with options, both in writing and orally from his advisers and cabinet members. He considers the written papers and listens to the oral arguments, but rarely makes a decision on the spot. Instead, the president's advisers announce that an issue is ready for a presidential decision, but that the president wants more time to reflect.

At the moment, natural gas deregulation is in such a state of suspended action. In this, as with other issues, the delay occasioned by Reagan's sometimes prolonged private considerations appears to outsiders to be mostly a means of seeing a politically propitious timing for a decision.

On questions that have reached this stage, the president can announce a decision at any time even though days or weeks may have passed since the issue was last described as being on a front burner.

While the president's day-to-day role is sometimes unclear, there are some important decisions on which Reagan acts from strong convictions and takes a leading role.

In a tough choice between lowering the budget deficit and cutting the rate of increase in defense spending, Reagan came down strongly last August on the side of a large defense buildup. He did not want to trim his defense plans and he stood firm.

Despite his goal of balancing the budget, Reagan has stood equally firm against recommendations that tax revenues should be raised. The president believes in the supply-side economic theory that the tax cuts he won last summer will eventually stimulate growth and new revenues. Reagan resists taking away with new taxes the money people will receive from his tax cuts.

Reagan's decision to resume grain sales to the Soviet Union was another example of an issue on which he felt strongly committed and played a leading role. He had campaigned against President Carter's grain embargo, which he thought placed an unfair burden on farmers.

From the day he took office, he made no bones about his desire to lift the embargo despite his contradictory hard-line policy toward the Soviet Union.