Forty-eight years ago, when she was 15 years old, Grace Paley entered the freshman class at Hunter College. But she dropped out after a year, horrifying her parents. ''They didn't know that 25 years later everyone would be doing it,'' Miss Paley recalls, smiling. Her worried parents insisted that she take a typing course so she could support herself. They may have known she would become a writer - she had been writing poetry since she was a small child. They may have suspected that their feisty daughter would also become a social activist. But they never dreamed she would also become a teacher - one of the most popular on the Sarah Lawrence campus in Bronxville, N.Y.

Neither did she. Miss Paley began her teaching career for the same reason that many creative artists do: to make money. Her teaching job, which she felt lucky to get without a college degree, was taken to subsidize her writing, not to sustain and nourish her as did the writing itself. ''You become a writer because you need to become a writer - nothing else,'' she says. ''Any work that you do that isn't writing is taking you away from writing.''

But Miss Paley says she found that she also liked to teach - and that teaching enriched her work by putting her in touch with another generation. ''I hardly ever write of a single generation,'' she says. ''I'm interested in intergenerations - the young people and the old -because I'm more interested in history than I am in psychology.''

But mostly, she says, her writing benefits from her exposure to new voices and new ideas. ''Young people read different books and think about different things,'' she says. This is important to her, she says, ''because as a writer one of your jobs is to bring news of the world to the world.''

The 63-year-old author, antiwar activist and feminist has been teaching for 20 years. She has taught at Columbia and Syracuse universities, and she has been teaching a weekly class at City College for two years. But her main teaching job has been at Sarah Lawrence, where she has taught writing for 18 years. Her classes there are extremely popular. Her students say there is intense competition to get into them and the administrative staff reports there are always at least five times as many applicants as openings. ''To me, teaching is a gift,'' she says. ''because it puts you in loving contact with young people. You don't get that from your children's friends, and your children go ahead and grow up on you, so it is a present that these 18-year-olds come into your life.''

Miss Paley's most recent collection of short stories, ''Later the Same Day,'' has been nominated for the Penn/Faulkner Award as the best work of fiction published in 1985. Earlier collections include ''The Little Disturbances of Man'' and ''Enormous Changes at the Last Minute.'' She is known for her lean, tough prose, her strong individual voice and her wit. Not surprisingly, many of these characteristics carry over into her ideas about teaching, as expressed in answers to questions:

Q. Can you teach a person who knows how to write a good school essay how to write creatively?

A. You can do that easier than you can teach a creative person how to write a good school essay.

Q. Is it true that the best advice for a young writer is to write about what he knows? A. I think it's what you don't know about what you know that's interesting.

Q. What is the hardest problem in teaching creative writing?

A. It's trying to keep a class of bright kids dumb.

By this last she means trying to keep them able to look at things clearly, to look straight at life without embroidering upon it. ''I don't mean they shouldn't make things more beautiful -they should do that if they want to. But they must remain honest. That's what writing literature really teaches. The story is a big lie. And in the middle of this big lie, you're telling the truth. If you lie, things go wrong. You become sentimental, opaque, bombastic, you withhold information.''

Because she believes that writing teaches honesty, she has an easy answer to the question of whether creative writing can really be taught: she thinks it can. But she also believes that the question is misleading. When people ask it, she says, they are really asking, ''Can you make a writer?''

''When you ask, 'Can you teach math?' no one means can you make a mathematician,'' she says. ''If a math teacher finds a brilliant student it's wonderful, it's rare. In writing I assume there will be some talented students and some less talented. The most talented people won't always become the writers. For the people who won't become writers, I hope to show them how literature is made - to understand it better, love it more, help them think about it and about other things too, because you write about things, not just words, about a certain subject matter. For those who do want to become writers, I hope to help them understand the process and learn through mistakes and to infuse them with my own feelings that it's a wonderful life.'' FOR Miss Paley, the key to her approach to teaching writing is respect for the process of becoming a writer. As a young woman, when she returned briefly to college and took a writing course, she was asked to leave the class because the professor was offended by her work. She says she can't remember exact reasons now; perhaps it was her use of some ''bad language.'' In her own classes, she stresses to her students that they must take risks, that there are no wrong words, no forbidden styles. She tries to emphasize that mistakes are profitable. She thinks that this is the greatest advantage of having writers teach writers - that they remember their own process of becoming artists, and are thus better able to see their pupils' work as part of a trajectory.