The three-character play is set in the drawing room of a flat located on Cromwell Road in London. Shaw describes Henry Apjohn as "a very beautiful youth, moving as in a dream, walking as on air," while Aurora Bompas has "an air of being a young and beautiful woman but as a matter of hard fact, she is, dress and pretensions apart, a very ordinary South Kensington female of about 37, hopelessly inferior in physical and spiritual distinction to the beautiful youth." The third character is Aurora's husband Teddy, "a robust, thicknecked, well groomed city man, with a strong chin but a blithering eye and credulous mouth."
Aurora is distressed because she has misplaced some poems, in which she is identified by name, written for her with declarations of love by the impetuous Henry. She suspects her sister-in-law Georgina stole them from her workbox and is concerned she will read them to Aurora's husband Teddy.
Henry suggests they confront Teddy with the truth, "quietly, hand in hand" and depart - "without concealment and subterfuge, freely and honestly, in full honor and self-respect" - for their planned evening at the theatre. (Henry has purchased tickets for Candida - the popular Shaw comedy which Henry and Aurora's situation closely resembles - because Lohengrin was sold out.) The two engage in a discussion about the merits of revealing their affair until Teddy arrives and confronts Henry with his poetry.
The young man tries to convince him they were inspired by Aurora, the goddess of dawn, rather than his wife, and assures him he has no interest in the woman Teddy married . . . which the cuckolded man finds so insulting he demands Henry admit how desirable Aurora is. Henry finally confesses his love for Aurora, which pleases Teddy so much he proposes he have the poems published on "the finest paper, sumptuous binding, everything first class" as a tribute to his wife. "What shall we call the volume?," Teddy asks. "To Aurora, or something like that, eh?," to which Henry replies, "I should call it How He Lied to Her Husband."

Question: What does Teddy want to do with the poems in the end?
Answer: Have them published on the finest paper and named after his wife.
Alternative answer: He wants to publish them in a fine bound volume.