Gary Hart has learned much about American politics in the past four months. Recall last May: Where, in a doomed effort to rescue his collapsing presidential campaign, did Hart un-smartly go? To a New York meeting of newspaper publishers and princes, that's where. So sympathetic were the press barons to the Coloradan's side of the story that within three days Hart became a former presidential candidate.

But now it's September. Hart's current task is no longer the rescuing of the candidacy; it is to redeem his own public career, which is no easy assignment. Last week, in logical pursuit of that objective, Hart took his case to television, to the "Nightline" confessional of Ted Koppel, to the country. That was smart. In the politics of 1988, television is the ball game.

The original for an effort such as Hart's, of course, was that Sunday night in 1952 when the only American besides Franklin Roosevelt ever to be nominated five times by a major party for national office came up with his own variation of the Fala strategy FDR had himself successfully used eight years earlier. ''It was a little cocker spaniel dog in a crate . . . sent all the way from Texas -- black and white, spotted, and our little girl, Tricia, the six-year-old, named it Checkers. As you know, the kids, like all kids, loved that dog, and I just want to say this, right now, that regardless of what they say about it, we're going to keep it.''

Of course, ''they,'' having never previously heard mention of that lovable pooch, had never said anything about it. But when after that speech, a million Americans called, wired or wrote to register their support of him, Richard Nixon conclusively proved the political clout of TV.

Television's influence on our politics and our culture has been pronounced. Thirty years ago in Little Rock, it was TV news, and John Chancellor in particular, that showed America the ugly, hateful face of racism. On both the Saturday and Sunday following Nov. 22, 1963, the average American watched TV for 10 hours. And TV comforted a nation in its loss. After the Democrats' bloody riots in Chicago when Hubert Humphrey was nominated in 1968, enough voters decided that a party that couldn't run a convention probably couldn't run the country either, and Richard Nixon won the White House. In 25 years, the popular perception of the blue-collar worker dramatically changed from the lovably hapless William Bendix in the ''Life of Riley'' to Jackie Gleason's plucky Ralph Kramden to the ignorant bigotry of Archie Bunker as played by Carroll O'Connor.

But early returns indicate that in the campaign of 1988, TV will be even more dominant. Take the case of Republican front-runner George Bush, who, according to polls, more voters judge to be ''weak'' than ''strong.'' That particular negative is very nearly an occupational hazard for every occupant of the vice presidency, a derivative office that does not encourage forceful independence. So to prove that he is not weak, Bush publicly changed his position and agreed to accept William Buckley's invitation to appear on a televised debate.

On the Democratic side, where the candidates are even less known, televised debates could play a decisive role. Without cutting issues on which the candidates can distinguish themselves, voters must look to the personal qualities of character to make their assessment. Thus, the ability to be concise, precise and humorous, plus the good fortune to be free of distracting facial tics or mannerisms, could mean the difference in the early winnowing out of the presidential field. Because television news is even worse than the rest of the press in covering a field of a dozen candidates, TV will lead the press charge in narrowing to two or three the number of candidates still standing by the first of March.

Even in this TV era of politics, a candidate can still be victimized by Indecent Exposure. Probably no married politician ought to appear as a contestant on "The Dating Game" or in a cameo role on "The Young and the Restless."

In presidential politics, the candidate travels not from precinct to precinct or from city to city but from media market to media market. Given his own past problems with his date of birth, it is possible that by 1992 Hart could be too young to run for president. But if he still has a chance then, give TV the credit.