Hundreds of thousands of Africans turned out today to vote for Rhodesia's first black-led government and bring to an end 89 years of white domination over this war-weary land.

By midafternoon on the first day of polling, nearly 20 percent of the country's approximately 2.9 million black, white, Asian and colored voters had cast ballots despite scattered guerrilla attacks designed to discourage participation in the five-day election.

Seven years of war already has taken more than 14,000 lives, and practically all black Africans interviewed said the main reason they were voting was hope that it would end the fighting.

"It is the only alternative we have to the war," said a young farm worker just after voting in the small northern village of Mount Darwin.

"We don't know if voting will stop the war, but we are hoping it will," said a voter in another northern village, Dotito.

Two lines of ragged, bare-footed Africans snaked back and forth in front of the Dotito schoolhouse, men in one and women in the other. Some had been standing for more than five hours in the hot sun waiting their turn to put an "X" before one of four parties listed on a ballot they could not read and only barely understood by a set of symbols.

Rhodesian officials described the results as "very good", all across the country, although initial reports suggested the turnout varied from district to district depending on the strength in each area of black nationalist guerrillas opposed to the elections.

Bishop Abel Muzorewa, the black leader expected to emerge from the voting as the first prime minister of "Zimbabwe-Rhodesia," told a gather ing of international observers and correspondents tonight that they had come to witness the thing black Africans have been struggling to obtain for years: the right to vote.

"I am satisfied that the will of the people of this land is going to be triumphant," he said, calling on the outside world to recognize the new blackled government "whatever the percentage poll we get."

The first day's turnout seemed to indicate that more than 50 percent of the black electorate probably will participate by Saturday in the election for the 72 Africans who will sit in the new 100-member parliament.

Voting was particularly heavy here in the capital, where long lines formed at polling stations in black townships surrounding the city. Crowds were so big that some were unable to cast their ballots before polls closed at 7:30 p.m.

The polling here seemed to be a festive occasion for the most part. African groups supporting one or another of the five black parties involved in the election danced and sang outside the stations and held up posters of the leaders.

But about 500 black students held a peaceful demonstration on the campus of the University to protest the election. One carried a big sign saying: "Cuba save our soul and stop the rot."

In guerrilla-inhabited rural areas, the voting varied greatly. In one tribal trust land, or African reserve, near Fort Victoria in the southeast, only 155 persons of the 40,000 living there had turned up by the end of the day.

On the other hand, in the northern Mount Darwin and Centenary area, where the war first began in December 1972, around 25 percent of an estimated 90,000 potential voters showed up at the polls the first day.

The Fort Victoria area was also the scene of several incidents. Guerrillas shot at one group of 150 Africans lined up at a polling booth, attacked two other voting booths and set up roadblocks to prevent people from reaching stations in some areas.

Reporters also learned guerrillas had hit seven African compounds on white farms in the northern Centerary area Sunday night, telling blacks not to vote and killing four and wounding seven as a warning to others.

In western Rhodesia, initial reports seemed to indicate that very few members of the Matebele people, who make up about 17 percent of the population, were voting. Police reportedly arrested over 900 persons in Bulawayo, the area's main city, shortly before the election. They were said to be organizing a campaign to get Africans to spoil their ballots. Most were supporters of the banned guerrilla organization. the Zimbabwe African People's Union (ZAPU) of Joshua Nkomo.

The Rhodesian government has mobilized 60,000 to 70,000 police and army troops to prevent the guerrillas from attacking the 2,000 polling points throughout the country.

The government also has gone to great lengths to make it possible for the nearly 30 foreign correspondents and 70 observers here to witness the polling, hoping to convince them that it is fair and free so that the new government will gain international recognition.

Reporters and observers spread out in four different directions to watch the process, traveling first by plane and then by helicopter and armored vehicles to remote points. They were taken mostly to see voting in urban areas, around the 5,700 white farms and at some of the 190 Protected Villages, the Rhodesian version of American strategic hamlets in Vietnam.

These are the areas where the government is assured of the highest turnout because of its ability to protect the population and get it out to vote.More than one million of Rhodesia's 6.8 million black Africans live in the urban areas, 1.5 million on white farms and 350,000 to 400,00 in the protected villages. CAPTION: Picture, Rhodesians acclaim Bishop Abel Muzorewa at black polling place in Salisbury. AP