One day last year a freshman senator wandered onto the floor as the Senate was voting to resolve a turf fight between two committee chairmen and noticed that Majority Leader Howard H. Baker Jr. was missing from his usual perch on a table at the front.

He found Baker hunkered down in a third-row chair and asked why. "There's an old Tennessee saying," responded Baker, grinning. "Ain't got no dog in that fight."

Baker had more glittering moments during his first year as den mother, father confessor and big brother for the fledgling Senate Republican majority. But the story, told by Sen. Slade Gorton (R-Wash.), helps explain how Baker has combined easy-going Tennessee mountain charm, legislative street-smarts, seemingly inexhaustible patience and a keen instinct for winnable dog fights into a growing reputation as the most resourceful, successful majority leader since Lyndon B. Johnson.

If Johnson won by twisting arms, Baker wins by stroking egos.

Sitting in the same office he held as minority leader, having appeased Sen. Robert C. Byrd (D-W.Va.) by letting him keep the corner suite he held when he was majority leader before the 1980 elections, Baker was asked to reflect on his own style of leadership.

He squirmed a little, talked about "reasoning together" and "personal relationships" and then recalled an introduction that Sen. William V. Roth (R-Del.) once made for him: "Howard Baker is like a political neutron bomb. He destroys his opponents and leaves their egos standing." Not quite true, Baker added, but "it's the highest form of flattery."

It is hard to imagine the short, stocky, low-key and amiable Tennesseean, a self-described "camera nut" who seems happiest when he is running around snapping photographs of other important people, as any kind of explosive device.

But his is a highly personal and collegial style of leadership that keeps senators in line by making them feel important and needed, which is how senators like to feel.

He spends at least three-quarters of his long days on Capitol Hill with individual senators, and rarely does he end a meeting without "handing out bouquets all around the table," according to associates. He uses people in ways they don't seem to mind, protecting his own political capital while committee chairmen and others venture forth to test the minefields.

"Whatever it is, he lets you think you're doing it, not that it's being done to you," observes Senate Budget Committee Chairman Pete V. Domenici (R-N.M.). But, says Banking Committee Chairman Jake Garn (R-Utah), he's "upfront . . . with no hidden agenda."

"He never tries to upstage a committee chairman," says Senate Finance Committee Chairman Robert J. Dole (R-Kan.).

Virtually born to politics, a "congressional brat," as one friend puts it, Baker knows Congress and its inner dynamics as well as anyone. His father and stepmother served in the House from their rural district in Republican eastern Tennessee (where his grandfather was a judge and his grandmother a county sheriff).

His father-in-law was the late Senate Minority Leader Everett M. Dirksen (R-Ill.). His daughter Cissy is now running for the House.

He passed up his father's House seat to take a long shot at a Senate seat in 1964, and built on a strong first showing to win election to Tennessee's other Senate seat in the still strongly Democratic state in 1966. He was elected minority leader in 1976 on the third try but was growing so bored that friends say he almost did not run for reelection in 1978. His boredom was instantly relieved when the Senate turned Republican in 1980.

Only a year ago when Baker made the jump from minority leader to majority leader, there was a widespread impression that he was on probation, elected only at the sufferance of the suddenly swollen ranks of GOP right-wingers who were suspicious of his conservative credentials.

Baker was chosen unanimously only after he solicited, and got, the active support of Sen. Paul Laxalt (R-Nev.), who was, by virtue of friendship and political loyalty, President Reagan's "man in the Senate." There was also talk that it would be Laxalt, not Baker, who would really be running the Senate.

Now, as Baker begins what is expected to be a much tougher second year as majority leader, he is clearly in command, with Laxalt playing a supportive role that is apparently comfortable to both men. "A 10 plus," says Laxalt of Baker's performance.

Early in last year's session, Baker headed off a revolt among nervous freshmen over a necessary but politically distasteful proposal from Reagan to raise the debt limit, using Senate elders like Strom Thurmond (R-S.C.) to soothe them in a way that made Thurmond feel needed, the freshmen comfortable and Reagan grateful.

"That was perfectly dreadful," Baker said in an interview, recalling how he had to tell the White House that he did not have the votes to pass the debt bill and did not know where to get them. "It was all I had left--to bring in the hierarchy."

And that is what he did. "I'll never forget Strom Thurmond. He looked at the eight to 10 freshmen and he said, 'Gentlemen, I understand you are concerned that you always opposed an increase in the debt limit. Some of you served in the House and you never voted to increase it. Well, neither have I. But I never had Ronald Reagan for president before, so I'm going to vote for it and I believe you should too.' " The measure passed.

Through the even larger budget battles of the year, this often protracted, sometimes clumsy groping for a consensus paid off so handsomely that the Democrats declaimed in forlorn envy that the Republicans did everything in "lockstep." Said Appropriations Committee Chairman Mark O. Hatfield (R-Ore.): "He was the catalyst who brought us together."

Hardly a budget battle that mattered was lost in the Senate, giving Reagan a secure base from which to operate successfully on the Democratic-controlled House.

In some cases, Baker, joined by major committee chairmen working in impressive concert, was able to pull the administration back from the brink of congressional defeat, as in the case of its proposed Social Security benefit cutbacks.

Moreover, Baker is regarded by his colleagues as largely responsible for having saved the administration from an embarrassing, largely self-inflicted foreign policy setback on the sale of AWACS (Airborne Warning and Control System) planes to Saudi Arabia. "It couldn't have been done without him," says Laxalt.

Baker was less successful in fending off the administration's "September offensive" for additional budget cuts but was instrumental, in weeks of painstaking and painful negotiations, in getting them cut back to digestible proportions: a "half-loaf" that enabled Reagan to claim a victory without really having won one.

Comments from two ends of the political spectrum are indicative. From the liberal end, Senate Minority Whip Alan Cranston (D-Calif.) calls Baker "remarkably effective" as well as "fair." Sen. John East (R-N.C.), one of the most conservative of the freshmen, says he has "nothing but the highest praise" for Baker and adds: "He carried a great deal of water for Ronald Reagan."

For all the dazzling reviews for his debut, however, his patience and consensus-style leadership may be severely tried if, as many expect, Reagan's second-year program and "social issues" like abortion and school prayer exacerbate the divisions in Republican ranks that Baker helped paper over last year.

"If there is any criticism of Howard Baker," said an otherwise admiring committee staffer, "it's that he's not mean enough," implying that his patience sometimes creates impatience in others.

Senators upon whom he has lavished his patience and ego-massaging charms disagree, but even last year he often walked a fine line--between congressional imperatives and obeisance to his president, between conflicting interests within the Senate itself and between his own moderately conservative tendencies and the more all-out brand of conservatism espoused by Reagan and the GOP's far right.

He got off to a shaky start this year by pushing a measure to allow Senate sessions to be televised, rankling some Republicans and risking an embarrassing personal defeat if the Senate shoots the proposal down. To Baker it is an important step in putting some polish on the Senate's tarnished reputation as the world's greatest deliberative body, which he has set as one of his goals.

More importantly, Senate Republicans are in open revolt over Reagan's proposed budget for fiscal 1983. Baker stepped out front early, welcoming a proposed alternative from the Budget Committee's ranking Democrat, Sen. Ernest F. Hollings of South Carolina, that administration officials promptly denounced. It is a vise, and Baker is right in the middle.

Baker, who had unsuccessfully challenged Reagan in the early 1980 primaries, got off to a good start with the new president last year.

In one of their early conversations after the inauguration, Baker recalls, "he Reagan was hedging a little to the effect that , 'Well, this may be at variance with what I understand your position to be.' I said, 'Look, Mr. President, there are some things on what you and I may disagree and if we do and if I must take a separate position, I will try to let you known in advance. But you should also know that on every issue where it's a close call I'm going to resolve the issue in your favor.' "

Baker acknowledges he had to make what he calls "delicate" choices "a lot of times" last year. While he declines to go into details, he is clearly uneasy over the administration's civil rights record and said, albeit after the fact, that social program appropriations may have been cut too severely last year. He has lost on some battles but won on others, most conspicuously on submitting the issue of Social Security cuts to a bipartisan commission.

Baker rides high in the Senate because he has been able to deliver on critical issues for both the White House and Senate Republicans, blunting the arguments of those who might prefer a leader of greater ideological purity.

But if Reagan is now asking Congress to deliver the undeliverable, as some Republicans fear, Baker could suffer too as dissension undercuts his ability to achieve consensus and emboldens the far right.

It is still suspicious of Baker but less agitated about him. "Because of his record . . . the residual hostility is still there," says Paul Weyrich, one of the New Right's leaders, claiming also that Baker has treated the New Right's agenda as "second-class issues."

Moreover, some of the very qualities that help Baker as majority leader--a compulsion for compromise and a cautious, reasoned personal style that can lull a crowd as easily as it charms an individual--could get in the way of his still-strong ambition to be president.

For his disastrous presidential campaign in 1980, Baker can blame the fact that he stayed too long in Washington, apparently hoping the Senate, along with a planned showdown on the strategic arms limitation treaty (SALT) that never materialized, would give him a compelling platform for advancing his candidacy.

But friends cite other reasons as well: "advanced disorganization" when it cames to national campaign strategy and a public record of ideological "flexibility," exemplified in 1980 by opposition to SALT coming just after he supported the Panama Canal treaties, that creates an aura of inconsistency if not outright expediency.

Passed over at least three times for even the GOP vice presidential nomination, Baker appears to be feared more by the Democrats, many of whom rated him as their biggest threat going into 1980, than he is sought by the Republicans.

"I make no bones about it, I want to be president," Baker said the other day in an interview.

But, given his conviction that he got drummed out early in 1980 because he stayed too long at his Washington duties, he believes he would have to resign from the Senate at the end of his year, which he appears reluctant to do.

1984? "That's too far in the future to look."

Patient man that he is, he nonetheless concedes "the fates may be against me." But, he added, his back toward the window looking out over the Mall leading toward the White House, "this ain't no bad job either."