Michelle Jackson has played by all the rules.

In her search for a job since graduating from Coolidge High School two years ago, she applied at two hospitals, private employment agencies on K Street NW, an insurance company, the District of Columbia employment service, a newspaper, American University and other places she no longer recalls.

Last week she sat in a church at which her community leaders had scheduled a job fair and said, without much hope, that a man from an insurance company had said he might call her back.

"It's a little funny," she said. "Always they want to know what experience I have, but they won't hire me, so where I do get it?"

Jackson's experience is common this year in Washington where thousands of teen-agers are looking for jobs but finding none. By all accounts, the search grows less rewarding each year. The unemployment rate in the city for blacks from 16 to 19 years old has risen steadily and projections are not encouraging. Even with economic conditions expected to improve next year, the city's Manpower Administration estimates that one of four teen-agers actively looking for full or part-time employment rate of 25 per cent or higher, even in good times. Despite a wide array of official programs that promise counseling, training or placement, for many there are no jobs.

The gap between promise and reality is evident at the jobs minicenter in Anacostia High School. On a long rack are displayed special "Popeye" comic books describing, in simple phrases and pictures, the wonders of careers as computer, engineering and secretarial workers. One cover depicts Popeye carrying Swee'pea into an employment center. Popeye says: "There are careers for all kinds of people in offices, Swee'pea."

Phyllicia Hatton, who advises Anacostia youths seeking jobs through the minicenter, knows better. Hundreds have failed out forms there this year and left without encouragement. Three of four, she estimates, become only names in a file.

Across town, the Southwest Community House Employment Office put a Job Fair in a church last week. Tables and booths were set up for employers to interview young job-seekers. By mid-afternoon, the room was virtually empty.

"It's looking bleak," said Joan Barrett, a community house counselor. "We had over 100 kids come in today, so as far as the community involvement is concerned this was a success. As far as employer involvement, it failed. We sent out 25 letters to prospective employers asking them to attend. We got responses from five. Some of the others said it was no point sending anyone to the job fair because they did't have any jobs to offer."

Those who look for jobs through regular channels follow a bewildering route from personnel office to placement center at the Manpower Administration. Anthony Prether, 18, had prepared for his graduation from Anacostia High School by starting the job trek last fall.

Standing under a tree on the school grounds last week, he ticked off the names of 25 places where he submitted applications: "Sears, Montgomery Ward, Ginos, Hechts, K-Mart, Drug Fair . . ." None called back. He finally landed a job microfilming checks in a bank because his cousin worked there.

Job seekers profess widespread desdain for the employment service operated by the Manpower Administration. "I've given up at the employment office," said Angela Martin, 19, a 1976 graduate of Ballou High School. "I went down there when I got out of school and waited and waited just for someone to talk to me and then all that happened was I filled out a form and I haven't heard anything yet."

Some no longer seek work.

Often referred to as "discouraged" persons, their numbers are as obsure as their label. The Manpower Administration estimates the total of "discouraged" unemployed at 36,000, with only grim guesses about how many youths are among them.

Earnest Spellman, 19, a high school graduate had been a member of the unemployed labor force for two years. Last Decemebr, he recalled, was cold and he stopped looking for work.

Now, he says, he can usually be found "hanging out" on Good Hope Road near Martin Luther King Avenue, browsing through a late-night record shop, not planning to buy anything, looking for a party but not really interested in going, and passing time.

"What am I supposed to do? There are no jobs. At least that's what they tell me, and I can't make 'em give me one," Spellman said.

His friends, leaning with him on a car parked in a service station lot laugh and say, "Right on."

They are not eager to discuss the situation, but one said, "I'm taking a break. Everybody needs a break. Hell, you get tired of hearing those tired lines. Just cool out and take it easy for a while."

"I don't have a car," Spellman said. "There were places like Rockville where I could find work, in some of those offices . . . yeah, janitorial . . . but how I'm gonna get a car without a job? Then you say to yourself, hey, you know, slow down. It's costing money just to look.

"I'll always have a place to stay and a little something," he says with a macho smile. "I'm just laying for a job."

Teen-age unemployment among blacks is a national epidemic that grows worse almost regardless of economic coditions. The rate increases in good times and bad. nationally, the rate has risen from 26.3 per cent to 37.1 per cent in the last 10 years. In Washington last year, the teen-age unemployment rate was 35 per cent for blalcks.

In Washington, as in other central cities with large black populations, there is evidence that large numbers have become discouraged and have stopped looking. NationallY, about half of all those aged 16 to 19 are considered in the labor force - either employed or looking for work. In Washington, only one-third are in the labor force.

Economists agree that the hard times fall hardest on the young looking either for full-or part-time jobs and that the recession of the early 1970s has aggravate an already bad situation for them. Ralph Smith of the Urban Institute has estimated that one of four job losses caused by the recession has been suffered by a teen-ager.

Recession does not mean only jobs that are more scarce. It also means that out-of-work adults start snapping up low-level jobs in shops and service stations that youth ordinarily seek. The nighttime salesclerk's job suddenly looks god to the older man whose office job has folded.

"I used to be that if you went into a shoe store at night the chances were that it was a kid who waited for you," said Mattic Tayloe, head of youth services for the Manpower Administration. "Now it's an adult.They need those jobs."

As in other central cities, Washington has lost thousands of jobs to the suburbs in recent years, many of them laboring, clerical and food-service jobs for which teen-agers customarily strive. New jobs available usually are skilled ones requiring education and training above the level of many city teen-agers. There has been no surge of fast-food marts in the city suburbs - one reason why the suburban teen-age unemployment rate is far lower than that of a city. That rate for the entire area is about half that of the city.

This year, summer jobs for youth are becoming available slowly. On the blackboard in her Anacostia minicenter, Phyllicia hatton has written the names of companies that offered summer slots. "But when we call them up now, they seem not to know what we're talking about. They say they aren't hiring now. It gets very discouraging," she said.

Normally, city agencies and the federal government help to take up some of the summer slack with special job offerings. They are offering fewer this year than in the past, said Manpower's Taylor.

"We placed about 300 to 400 with the city last year. This year not only single one has offered to take one of our applicants. I guess it's the budget strain. The federal agencies are slower to offer jobs, too. I'd guess we are running about 50 per cent behind where we were last year," Taylor said.

Taylor considers a good year one in which Manpower places hal of the summer applicants. She doubts the target will be reached this time.

Various experts have noted that many teen-agers now spurn low-level jobs they once filled. Dishwashing and domestic cleaning work cn carry a stigma of servility often rejected by youth who look hard for jobs that offer training for something better.

Michelle Jackson, the young woman who had made the rounds for two years without success, is frustrated but there are jobs she will not accept. The job bank, she said, "only had stuff dealing with foods, hot grills, you know. I don't want that.I can do something more useful than food. There's no way I could advance in that."

She worked for six days as a waitress in an Army club. "It was too hard. Ten hours a day and lifting heavy trays of dishes into the dishwasher. And two of us waiting on 500 people and all of then velling, 'Hey, you, you, you,'" she said.

"Most kids will take anything," said the minicenter's hatton, "but some refuse cleaning jobs. They feel they're undignified. I tell them they'd better take what they can get, or they'll be standing in the streets all summer."

For some, ironically, the main obstacle to getting a job is their parents' income. many federally-subsidized youth jobs in schools, libraries, parks and the like can be filled only by children of families whose annual income is below the official poverty level of $5,800.

Manpower's Taylor said, "Half of the kids registered here are over the poverty level. When it really gets rough is telling a kid whose mom is a GS-3 secretary he can't get a job when they're scuffling to get by. It's a big problem for middle-class families who started out from meager beginnings. They see their child heading back to the poverty they came out of."

One who has encountered that roadblock is Alfred Moss, a 10th grader at Anacostia High School who has tried three times for summer work and failed.

"The word around here," he said, gesturing around the school playground where he was lounging, "is that you have to be on welfare to get a job. You've got be be a low-income family."

His friends tell Moss to get around that by fibbing. "What you do, they say, is just cut your daddy's income in half," he said.