When White House chief of staff Donald T. Regan sat down alone with President Reagan on May 13 to make final decisions on the administration's tax-simplification plan, it was clear evidence that the one-time treasury secretary and Wall Street businessman had become the strongman at the White House.

Regan's assumption of power has not been without its missteps. Along the way, the assertive executive has had to learn some of the lessons his predecessors learned. Regan acknowledged in an interview last week that he is "still on a learning curve."

One of those lessons, one senior administration official said, is "the necessity of keeping Defense Secretary Caspar W. Weinberger as far away from the president as possible." The official said Regan shares the view of some GOP congressional leaders that Weinberger has been too intransigent on the defense budget, too tardy in spotlighting wasteful spending at the Pentagon.

There is widespread agreement that Regan, after a shaky period, has put a distinctive stamp on White House operations. "Regan boarded a flying airplane, and it took him a while to find the controls," one White House official said last week. "But he is clearly the pilot now."

What remains unanswered at this early stage is whether he has not just the strength but the skills to guide Reagan successfully through a potentially perilous second term. Regan has been on the job four months, but his power has been asserted most clearly since mid-May.

One reason is that the first part of Regan's tenure was dominated in large part by controversy over the president's visit to the Bitburg cemetery in West Germany, where 49 members of Hitler's notorious Waffen SS are among the dead buried there.

Another reason is the departure of former deputy chief of staff Michael K. Deaver. Since Deaver's resignation, Regan has taken control of White House scheduling operations and makes a point of reviewing drafts of the president's speeches.

Finally, the tax plan that the president sent to Congress last week originated in Regan's Treasury Department last fall. And, as White House chief of staff, Regan was instrumental in shaping the final proposal. His advocacy of a provision that would allow companies to take a 10 percent deduction for dividends prevailed over treasury opposition.

Regan's admirers say he has brought a streamlined corporate-management style to a White House frequently marked by high-level feuding during Reagan's first term.

His critics complain that he lacks the deft political touch of his predecessor, Treasury Secretary James A. Baker III and that he does not delegate responsibility adequately. They also say sniping continues between Regan and both communications director Patrick J. Buchanan and national security affairs adviser Robert C. McFarlane.

But Regan, 66, has shown the ability to learn from his mistakes. "You get isolated in the White House," said Stuart K. Spencer, a longtime Reagan political adviser initially skeptical about the new White House team but impressed with its recent performance. "But Regan and the others are listening. They're very open, which is good. This is not a closed shop." Without announcing a change of policy, Regan appears to have muted the confrontational approach with Congress and administration adversaries that he and Buchanan were celebrating only a few weeks ago. Buchanan also has changed his approach. For several weeks he declined to talk to reporters, a practice he now calls "unrealistic."

But the new team has yet to acquire the skill of its predecessor in orchestrating "media events" to create a single, definite impression of presidential activity and purpose. Baker and Deaver tried, often successfully, to focus coverage on a single event that would advance the White House "theme of the day."

In the second-term White House there often are many events and many themes. On Memorial Day, for instance, an official said the White House team expected that reporters would emphasize Reagan's wreath-laying ceremony at Arlington National Cemetery because "so much was made of the visit to Bitburg."

Instead, much of the news coverage focused on a remark Reagan made in Miami, where he accused the Democrats of "segmenting America into warring factions -- over the years pitting white against black, women against men, young against old . . . . "

The remark was virtually identical to a comment President Jimmy Carter made in reference to Reagan on Oct. 6, 1980 -- and one that Reagan strategists used to portray Carter as mean-spirited.

Regan and Buchanan say they hope to limit the number of major issues they take on at any one time.

"I think anyone, not just Reagan, is better off when he's focused on one thing at a time instead of trying to do several major things," Regan said last week. "I think that one major theme should be struck at one time."

Regan is conscious of Baker's reputation as a skillful politician and about Baker's retailoring of the first tax plan, known as "Treasury I."

"Regan's ego works against him when the subject of Baker comes up," one administration official said. "Don's a good manager, a smart guy and a winner, but he's oversensitive to criticism, and this has led some of his people to say that Treasury I was a better plan and imply that the present version is a sellout. The present plan can pass, and Regan ought to be willing to give credit to Baker and let Treasury worry about the lobbying on the Hill."

Some officials say that, when the crunch came on decisions within the White House, Regan was as effective as Baker in dealing with the president, and nearly as pragmatic.

Regan sided with the Treasury Department and presidential assistant Edward J. Rollins in favor of a top tax rate of 35 percent, which put him in conflict with Buchanan, Rep. Jack Kemp (R-N.Y.) and other conservatives, who wanted it to be 30 percent.

Although conflicts in the current White House do not approach the dimensions of the battles between Baker and Edwin Meese III, now attorney general, in the first term and later between Baker and then-national security affairs adviser William P. Clark, several officials say that relations between Regan and McFarlane are cool.

The coolness briefly surfaced during the MX missile debate, when Regan suggested that he should go to Capitol Hill to negotiate with Sen. Sam Nunn (D-Ga.), leader of the effort to limit MX deployment. McFarlane, who has been administration point man on the MX for years, countered that he should.

Ultimately, Max L. Friedersdorf, the assistant for congressional relations, accompanied McFarlane to Nunn's office and the president talked to the senator by telephone.

"It was an example of where Regan wanted to do everything himself, even when someone else could do it better," said one official familiar with the conflict. "But he wound up making the right decision, which is what counts in the long run. Regan is in it for the long run."