Ellen Burstyn in a play of bookish humors and delight; 84 Charing Cross Road Starring Ellen Burstyn. Play adapted by James Roose-Evans from the book by Helene Hanff. Directed by Mr. Roose-Evans.

Problem: How best to convey the gentle serenity, reciprocal warmth of feeling , bookish humors and delights, and tender humanity of ''84 Charing Cross Road.'' Solution: Begin with Helene Hanff (Ellen Burstyn) seated at her typewriter in the ground-floor apartment of a brownstone in upper Manhattan.

It is a run-down brownstone, because Helene is a struggling writer and $40 -a-week script reader. As the curtain rises, she is pursuing her vocation of collecting secondhand books. She is writing to Marks & Co. of London in response to its advertisement in The Saturday Review of Literature. The time is 1949.

Thus begins the correspondence that lasts for 20 years. The letters between Helene Hanff and the people at the antiquarian bookstore who were to become her unseen friends resulted in the book which James Roose-Evans adapted for the stage. ''84 Charing Cross Road,'' which has run for more than a year in London, is newly arrived on Broadway at the Nederlander Theater.

The sociable adaptation brings together the principals in a remarkable correspondence. As the play progresses, the ocean separating them seems scarcely wider than the distance from Helene's apartment on one side of the stage to the cheerfully book-lined premises of Marks & Co. on the other.

The exchanges begin formally, with Helene addressing the London firm as ''Gentlemen'' and Frank Doel (Joseph Maher) signing himself ''F. D. for Marks & Co.'' Not too many shipments later, the irrepressible American has progressed to ''Dear Frank'' and ultimately to a saucy ''Dear Frankie.'' The British book dealer retains his dignity - but not indefinitely. Meanwhile, Helene is becoming part of the lives of what Frank calls the bookstore ''inmates,'' just as she is becoming part of theirs.

Helene is an exacting client. She scorns Keats, Shelley, Blake, and an abridged ''Pepys' Diary'' (which she pronounces ''Peppies''). She is grudging about Chaucer. But she dotes on John Donne, John Henry Newman, and an uncut Isaac Walton. One of her idiosyncrasies is always to pay in cash, since she trusts the mail delivery system more than their money orders.

The slangy New York bibliophile endears herself to Frank and the others by sending them food packages in the postwar years before rationing has been lifted in Britain. In return, she receives a handsome, embroidered Irish linen tablecloth.

As the letters accumulate and the orders are filled, one learns about the progress of Helene's career as TV scriptwriter (from Ellery Queen to the Hallmark Hall of Fame) and about lives of Frank and his colleagues. Cecily Farr (Ellen Newman) is going to join her Air Force husband in the Middle East, but not before sending Helene a recipe for Yorkshire pudding. Megan Wells (Jo Henderson) sets off for South Africa, which she finds disappointing. Frank's daughters reach maturity. His passing signals the end of Marks & Co. By 1971, when Helene achieves her dream of visiting London, the bookstore has gone out of business.

Considering its apparent limitations of format, ''84 Charing Cross Road'' abounds in liveliness and variety. Miss Burstyn is a most engaging Helene - sharp-witted and sharp-penned, fastidious in her literary demands, zestful and generous-hearted. Mr. Maher gives a beautifully shaded performance as the scholarly dealer who gets caught up in his singular American's quests and enthusiasms. Under Mr. Roose-Evans's direction, the correspondents and their letters become the expressive life of the play.

The production was designed by Oliver Smith (scenery), Marc B. Weiss (lighting), and Pearl Somner (costumes).