The maid of the title is red-haired, dog-loving Wilhelmina "Billie" Bennett, and the three men are: Bream Mortimer, a long-time and long-suffering suitor of Billie; Eustace Hignett, a shy poet who is cowed by his domineering mother but secretly engaged to Billie at the opening of the tale; Sam Marlowe, Eustace's dashing cousin, who falls in love with Billie "at first sight". The four of them find themselves together on a White Star ocean liner called the Atlantic, sailing for England. Also on board is a capable young woman, Jane Hubbard, who is in love with Eustace. Wodehousian funny stuff ensues, with happy endings for all except Bream Mortimer.
