THE POWER GAME: HOW WASHINGTON WORKS; By Hedrick Smith; Random House; 793 pages; $22.50.

Hedrick Smith, the New York Times-man, draws on his 26 years in the nation's capital to describe how political power has evolved and how presidents, members of Congress, lobbyists, journalists and other Washington inhabitants play the power game in the '80s.Smith, a regular panelist on PBS' "Washington Week In Review," recites a litany of anecdotes to support his contention that the power game has changed and that new rules are being written every day.

"The Old Order" is gone and the president is more powerful than ever, Smith declares; then in almost the same breath he shows us how the president and Congress keep trying to blunt one another's control.

The 800-page book is packed with insight on the recent Washington scene, but it is mostly a restatement of current events that will vanish as quickly as today's headlines. This book undoubtedly will land on coffee tables for a few weeks, become the topic of conversation during the pres-ent political season and then slide into obscurity after November. What will keep it from vanishing completely is Smith's attention to detail, his wonderful comparisons of the Reagan years to past administrations and his delightful personality profiles of politicians he has known.

Smith has done political scholars a favor by plugging the Reagan presidency into the power games of his predecessors. The references to Carter, Nixon, Johnson and Kennedy are retold tales, but when lumped in with the Reagan presidency the events of the past become reminders of why we voted for these men in the first place.

Reagan-haters will find plenty to cheer in Smith's recounting of the president's faux pas. Reagan supporters will find plenty of stories gleaned from the accounts of White House insiders who have churned out their own books. Consider this episode:

As the 1984 campaign was winding down, CBS correspondent Leslie Stahl prepared a tough, 41/2-minute piece analyzing how Reagan strategists used video "to create amnesia" about the president's record:

Stahl's producers had created a montage of Reagan video vignettes to illustrate her piece: Reagan cutting the ribbon at an old-folks home; greeting handicapped athletes; giving a hug to Olympic gold-medal winner Mary Lou Retton . . . relaxing at the ranch in faded jeans; paying tribute at Normandy to American GIs who had died in the World War II landing. . . .

"I thought it was the single toughest piece I had ever done on Reagan," Stahl said, recalling her apprehension about the White House reaction. "The piece aired and my phone rang. . . .

"And the voice said, `Great piece.'

"I said, `What?'

"And he said, `Great piece.'

"I said, `Did you listen to what I said?'

"He said, `Leslie, when you're showing 41/2 minutes of great pictures of Ronald Reagan, no one listens to what you say. Don't you know that the pictures are the overriding message? The public sees those pictures and they block your message. So in our minds, it was a 41/2-minute free ad for Ronald Reagan.' "

In examining Congress, Smith contends junior members of the House and Senate command as much attention as senior committee chairmen because of the increased power of political action committees and television. This makes for strange political alliances. It doesn't pay these days to upset your opponent across the aisle, Smith concludes; tomorrow he could be your ally. Of interest to Utahns:

When Orrin Hatch, a staunch Utah conservative, took over from Ted Kennedy, the Massachusetts liberal, as chairman of the Labor and Human Resources Committee, his staff had to train him to work legislation through his committee. "His mind-set of what you do in the Labor Committee is oppose Ted Kennedy," a senior Republican aide said. "Suddenly he had a big chunk of the Reagan program thrust on him, and he didn't know what to do." Other Republicans were accustomed to cutting personal deals with Democratic chairmen, but not to passing bills.

Smith has little patience for critics of the American political system. He faults the voter as much as the politician for many of the nation's ills. He believes much of what is politically wrong today could be resolved if voters would simply exercise their franchise more often.

Smith is upbeat about America's future. He expects "the power game" to keep changing, and he analyzes many of the "reforms" put forth by prominent Democrats and Republicans. Smith does not attempt to forecast which of the many roads the nation will move down, but he has dusted off the road signs so we can read them.