Kingston, Jamaica — The warm Caribbean sun breathes down steadily on this ''land of wood and water,'' seldom missing a day, creating an atmosphere of tropical splendor. Jamaica is a beautiful island, conjuring up a variety of images: reggae and limbo, sun-seeking tourists and Rastafarian cultists, white sand beaches, and mountains that look blue in the light of day.
But behind this idyllic scene is a troubled island where poverty and backwardness stalk and a fresh effort at solving these problems is under way.
Jamaica today is a testing ground - where an unashamedly free-enterprise government is seeking to prove that democracy and capitalism can provide a better life for the island's 2 million people than did a socialist system that ruled the island for the previous decade.
But the jury is still out as the two-year-old government of Prime Minister Edward Seaga seeks to prove the point.
The island is full of projects, though - and foreigners lending their expertise. The Israelis are on the scene with agricultural and mineral technology; Canadians are searching for oil; British farmers are putting honey farms into operation; Nebraska animal-feed people are providing the formula for using animal wastes for cattle feed; while Michigan university specialists are resurveying the whole island.
There's clearly a sense of activity, of motion, of things beginning to happen.
''We is on the move,'' proclaims a sign in Kingston, the sprawling capital city of the island. That view is echoed by Mr. Seaga, whose hand is in just about every project and program on the island. Indeed, he wears many hats. And he seems to be just about everywhere on the island.
Some say he is too intimately involved, that he manages to be in on such decisions as one made recently over the contents of Air Jamaica's new in-flight magazine.
Yet there is no questioning his good intent and his counsel. He gets high marks for both.
And Jamaicans as a whole seem to appreciate his ability. Opinion polls have, for the most part, been supportive of his role as prime minister. Moreover, most everywhere the visitor goes in Jamaica, he gets the feeling that Mr. Seaga is given high marks for the way he is governing.
But still, Jamaica's economy is lagging, hard hit not only by the island's near-bankruptcy when Mr. Seaga came to power, but also by worldwide recession, the high price for oil of the late 1970s, the decline in demand for Jamaica's bauxite, and other problems.
Unemployment remains high; the slums of Kingston look no better today than they did two years ago; there are signs of an ugly mood among some of Jamaican youth angry with their lot; and there are limited signs of resignation by some Jamaicans who say, as did Trevor Jones, a rugged-looking, jobless black man near Mandeville, ''we might as well forget change; it ain't gonna come.''
That is probably too negative a view. Change is coming, and has come. But whether it can come fast enough remains to be seen. Mr. Seaga recognizes that solving the unemployment problem is fundamental to the change needed - and it is here that he is putting special emphasis this year.
In the past two years Jamaica has made some headway on this, particularly in the tourist and agricultural fields. In tourism, the island's second major money earner, jobs are more secure today. ''We've seen a major improvement here,'' says Dr. Marco Brown, the parliamentary undersecretary for tourism.
Other tourist officials note that employment in the tourist industry increased 21 percent in 1981-82 as the flow of North American tourists to the island reached record proportions. The flow is continuing this year, and there is an expectation that close to 100,000 Jamaicans will be employed in this field by the end of 1983.
But still, too many Jamaicans - some 20 percent officially, perhaps 30 percent unofficially - are unemployed, and the number of underemployed is even higher.
''Not until this problem is solved,'' says the Daily Gleaner of Kingston, ''can Seaga regard his government as successful.''
Mr. Seaga knows it. He says that it must be solved this year - or else. ''If we don't (solve it this year),'' he says, ''there goes our opportunity.''
It is uncertain whether he will have the success on this score that he wants. The prime minister, however, can certainly feel success in his ability to restore confidence to the island.
Many Jamaicans who left the island in the years that Prime Minister Michael Manley and his socialist-oriented government were in power have returned - and more are coming back.
But equally important for confidence is the flow of foreign money, investors, and projects to the island.
The hotels here are full of these investors. It is estimated that they have brought some $1.2 billion in one form or another to Jamaica in the past 18 months. Moreover, Jamaica has benefited from United States government interest, and in particular the friendship that has developed between Prime Minister Seaga and President Ronald Reagan.
The US is crucial to the Seaga effort, and Mr. Seaga readily recognizes it.
He emphasizes the closeness of the two nations: ''We have followed a political and economic system very similar to that of the US,'' he said in an interview, speaking of Jamaica's parliamentary democracy, the market system in the economy, the deep respect for human rights, personal freedom, and similar life style that link Jamaica and the US.