George P. Shultz assumed the helm of U.S. diplomacy at a White House ceremony yesterday and quickly sailed into the stormy seas of Middle East and East-West problems.

Within an hour of his swearing-in as secretary of state, performed by Attorney General William French Smith, Shultz participated in a National Security Council meeting on East-West trade policies and their application to European countries.

Even before the 10 a.m. White House ceremony, Shultz met at the State Department with top aides to discuss forthcoming steps in the U.S. drive to break the impasse over a future home for Palestinian guerrillas trapped in West Beirut.

Today Shultz is to meet several Middle East experts, including former secretary of state Henry A. Kissinger, who has figured in recent speculation as potential Middle East emissary in the Shultz era.

President Reagan, welcoming his new chief diplomat in the steamy Rose Garden, said he was reminded of the old saying, "Let George do it."

He went on to say that Shultz is "a man of character and common sense, affable and yet decisive" and that he brings to the office "perhaps a deeper understanding of world economics than any previous secretary of state."

Shultz, in turn, promised to "muster every ounce of energy and intelligence and dedication" in performing his job. He said he would take as his touchstone and foundation a statement in Reagan's inaugural address that "no weapon in the world is so formidable as the will and moral courage of free men and women."

Other than his brief and very general remarks at the swearing-in, Shultz said nothing publicly in his first day as secretary of state. After a private lunch with family at State, he began a round of meetings with staffers and outsiders that is to continue today. Among his visitors yesterday, aides said, were John D. Negroponte and Joseph V. Reed Jr., U.S. ambassadors to Honduras and Morocco, respectively.

Shultz is to greet State Department employes officially and have his first large staff meeting Monday afternoon. The next day, he will participate in Reagan's meetings with two key Middle East foreign ministers, Prince Saud Faisal of Saudi Arabia and Abdal Halim Khaddam of Syria, who will be here as a delegation from the Arab League.

State Department officials said Shultz is also likely to meet separately with each of the two Arab ministers, whose heads of state received personal appeals from Reagan earlier this week for assistance in finding a new home for Palestine Liberation Organization guerrillas.

Officials held out hope that next week's meetings with Saud and Khaddam can facilitate progress on this issue, reportedly the sticking point of the Beirut negotations involving the PLO, the Lebanese government and U.S. special envoy Philip C. Habib.

The sources conceded that substantial movement toward arranging a future for PLO fighters is unlikely before the meetings here.

Wednesday, Shultz is to leave for the annual encampment of the Bohemian Club of San Francisco, sometimes called "the world's most exclusive summer camp" or "the world's most elegant stag party."

Aides said Shultz had planned to attend the affair, held in a redwood forest 65 miles north of San Francisco, long before being tapped three weeks ago to succeed Alexander M. Haig Jr. at State.

One of Shultz' personal guests at the closely-guarded private encampment is to be West German Chancellor Helmut Schmidt, a longtime friend. A major subject of their discussion is likely to be intensified strains between the United States and Western Europe on East-West trade issues, especially western contributions to the proposed Soviet-West European natural gas pipeline. Another Shultz guest, aides said, will be Singapore's prime minister, Lee Kwan Yew, a senior Asian leader.

After two nights at the encampment, Schmidt and Lee are expected to return with Shultz to the secretary of state's private residence at Stanford University for discussions over much of next weekend.

Among the others who are to attend the encampment in the redwoods, administration aides say, are Attorney General Smith and Defense Secretary Caspar W. Weinberger, formerly an associate of Shultz in the San Francisco-based Bechtel Group. Reagan, in an oblique and joking reference to the "Bechtel connection," referred at the swearing-in to "some criticism of your similar background to another member of my Cabinet. I admit we may be dipping from the same well to find quality people. I just want everyone to know that I'm fully aware that George and . . .many other high-ranking members of my administration, are all former Marines."