And everywhere that Reagan went, the press was sure to go . . .

''How dare they frisk us again!'' cried Sam Donaldson of ABC-TV in mock indignation as white-gloved Japanese searched the American reporters before letting them into the prime minister's residence. ''Don't they know we've already been checked by the US Secret Service?''

This was but one of a thousand small dramas played out on the periphery of President Reagan's trip to Asia. For even while the President worried about not flubbing a speech in the Diet or forgetting the names of his South Korean hosts, the 240-strong press corps traveling with him worried about getting to the action on time, recording the event, finding a telephone, sending the story, catching up with the President, recording the next event, finding a telephone, sending the story. . . .

Little do newspaper readers and television viewers know how much of what they see and hear about a presidential trip is due to a massive White House effort to take care of the hordes of reporters and cameramen and women who travel with the President. The press is screened, tagged, checked, transported, housed, fed, briefed - all but sung to sleep - by the White House press office, a service for which, of course, news organizations pay.

Although traveling as if in a cocoon, the newmen and newswomen seldom get within earshot of the President. A chosen few are allowed to travel aboard Air Force One, where presidential aides wander back from time to time and respond to questions, dutifully recorded by a small press pool. Nancy Reagan might put in an appearance, especially when the White House wants the cameras rolling for the morning TV news show (as it did when Mrs. Reagan showed off the two Korean children she brought back to the United States for medical treatment). The rest of the press fly in a separate plane - in this case a Pan American 747 - where they are pampered by the crew, eat more food than they can comfortably digest, and spend long hours playing cards, reading, typing, and catching up on sleep after sometimes going 24 hours or more without it.

On the ground the logistics are mind-boggling. Filing stories or broadcasting seems to become almost secondary to keeping track of schedules - pool assignments, briefings, bus departures. These are worked out to the minute. In Tokyo a portion of the circuslike drill for Thursday, Nov. 10 - involving three separate ''press pools'' - looked like this:

9:50 a.m. Press pool No. 8 assembles in Okura Press Filing Center.

10:20 a.m. Press pool No. 8 departs Okura Press Filing Center en route prime minister's official residence.

10:40 a.m. The President and Mrs. Reagan depart Meiji Shrine en route Akasaka Palace.

Press pool No. 6 accompanies.

10:45 a.m. Press pool No. 7 and rest of press depart Meiji Shrine en route Okura Press Filing Center.

10:50 a.m. Press pool No. 8 arrives prime minister's official residence and is escorted to pre-position area.

10:50 a.m. The President and Mrs. Reagan arrive Akasaka Palace and proceed to suite.

10:50 a.m. Press pool No. 6 is escorted to press holding area. . . .

Because it is impossible to have an army of journalists trailing the President at each function, a press pool of five to 10 people is assigned to each event. The pools are made up and numbered in advance so that each journalist knows which event he or she will cover. The pool invariably includes a television network and the major newsmagazines. The two writers in the pool take detailed notes - down to the color of the prime minister's tie, the look on the President's face, and the furnishings in the room where they meet - and quickly write up a ''pool report'' to be retyped, photocopied, and distributed by the White House press office. Official statements and speeches are put out in advance and made available with an ''embargo'' time. Briefings by the White House deputy press secretary and other US officials are held daily.

For the most part the operation goes smoothly. On this occasion the White House seemed to be outdoing itself in order to repair presidential relations with the press. Censorship during the Grenada invasion had left a residue of bitterness among the news media.

Even so, clashes with authority occur every now and then, like the argument that erupted at Kimpo Airport in Seoul over whether the writers (as contrasted with camera crew) were to wear an orange armband or an orange posy dangling from a neck chain in order to get into the National Assembly for the President's speech. The American and the Korean officials seemed to have conflicting orders. So, as the press buses were ready to take off, those with posies found themselves scrambling to get an armband which, it seemed, the US Secret Service had but did not want to give up.

''You'll hear about this when we get back!'' shouted an irate veteran newsman as he scribbled down a Secret Serviceman's name. Tempers cooled at last, and everyone was admitted.

Old hands on presidential trips give the Reagan shop high marks for organization, however. ''By comparison with the Carter people, they are a dream, '' one newsman commented. ''Carter had us staying in fourth-class hotels and his aides just didn't understand what the press needed. These people know their stuff.''

They know it, of course, because of all recent presidents, Mr. Reagan is the most adept at handling the news media, above all television.

Each event in Japan and Korea seemed as carefully planned for its impact on the early evening news as for its diplomatic objective. Events at the demilitarized zone separating North and South Korea - a morning worship service, a speech to combat troops at Camp Liberty Bell, and a visit to a guardpost inside the DMZ (where sandbags were appropriately added to accommodate a TV shot) - provided dramatic episodes for television back home.

En route home the journalists' spirits, after all the deadline pressures and sleepless nights, are jovial. The crew joins in the fun. ''Attention, please,'' says the pilot over the loudspeaker as the giant 747 gracefully lifts off. ''We've just gotten word from Air Force One that there's been a flood in Kyoto and we're going to make a stop there!'' A roar of laughter explodes throughout the plane.