Jay S. Hammond came out of the bush to become governor of Alaska. He had been a trapper, a pilot and flying instructor, and, depending on the season, a commerical fisherman and big-game hunters' guide.

A rugged-looking, broad-shouldered, deep-voiced man of 55, Hammond not only looks like somebody from the last frontier, he looks like one who can handle it.

Two months ago, acting as "any other Alaskan would have," as he puts it, Hammond rescued eight persons stranded when their light plane crashed in a storm near remote Illiamna. Hammmond managed to land his Cessna 170, equipped with skis, on a frozen lake, and flew two injured passengers and an infant to IIiaman. Another pilot flew the oter out.

Of all the governors at this week's National Governors' Conference, Hammond, a Republican, is clearly the least groomed for a political career. He spend most of his 32 years in Alaska ( he grew up in Vermont and was a Marine fighter pilot in World War II) simply living - some would say surviving - as a frontiersman. Once he crashed a small plane into a beaver house, causing the engine to explode. He walked away from that.

He did not walk away, however, from the pleas of a small group of friends who wanted him to run for the Alaskan House of Representatives in 1959, statehood year. He did it, though he had a "rather low pain threshold for politicians." He later was elected to the Alaska Senate, but left the state scene to become the $25-a-month, part time mayor of Bristol Bay Borough. Two years later his friends came calling again, asking him to run for governor.

Again, Hammond wasn't anxious. "I had a three percent name familiarity," he says, which wasn't surprising considering the way he never did hang around the population centers. He lives in tiny Naknek, about 300 miles southwest of Anchorage, and when he really wants to get away from it, in a log cabin he built himself in an isolated place called Lake Clark.

Married and the father of two teenage daughters, he had all the fishing streams he wanted, and the cabin to streans he wanted, and the cabin to putter in. But his friends persuaded him again to give up the good life.

With campaign funds totaling $800, Hammond took off by dog sled, Land Rover, and small plane ("I figured in a few week s I'd back in the hills where I belong") and knocked off every Alaska governor there ever was: Keith Miller and Walter Hickel in primaries, , then incumbent William Egan. He did not beat Egan by much, just 280 votes, and several recounts and weeks passed before it was offical. Nobody blamed Egan for not believing the outcome.

Hammond won because he seemed to be saying the right things at the right time: He cautioned about reckless development at the time of the oil boom and warned of losing the "quality of life" Alaskans had known. He made sense, especially, to conservationists, who perceived him as one of them. As governer, though, it's been tough sledding.

He's found himself in the middle between ecologists and development interests, between natives and newcomers, even between newcomers who come for the wilderness life. he's been criticized for state spending cuts; he says his major problems are the economy, which he wants tied less to oil, and how much land in the state is to be devoted to parks and how much to development.

Between meetings here in the past two days, he's been hurrying to Capitol Hill - despite his disclaimers on political life, he seems to know which way to turn - to sell a favorite project of his, a "cooperative management program" in which federal, state and private interests would get together to determine how the land will be used.

When he talks of this plan, he talks fast, excitedly, twice jabbing a finger into a reporter's lapel. He seems to like being governor. "I wasn't all that happy about getting in the swim the first year or two," he says, but now he wants a second term and is already campaigning hard for re-election this year.

While some at the governors' conference are thinking even of the presidency, Hammond is merely trying to hang on to his job. Opponents headed by Egan, are lined up, hoping to send him back to the bush. Hammond says three forces against him are former Interior Secretary Hickel, a Teamsters boss and the Anchorage Times.

If he doesn't make it, Hammond can begin life over, a peculiarly Alaskan proposition.