Juno and the Paycock takes place in the tenements of Dublin in 1922, just after the outbreak of the Irish Civil War, and revolves around the misfortunes of the dysfunctional Boyle family. The father, "Captain" Jack (so called because of his status as a retired merchant sailor and his propensity for telling colourful sea stories), is a loafer who claims to be unable to work because of pains in his legs (which mysteriously appear whenever someone mentions work to him). Despite his family's poverty, Jack spends all his time and money at the pub with Joxer Daly, his ne'er-do-well "butty," instead of looking for a job. The mother, Juno (so called because all of the important events in her life took place in June), is the only member of the family currently working, as daughter Mary is on strike and son Johnny is disabled, having lost his arm in the War of Independence. Mary feels guilty about dumping her boyfriend and fellow striker, Jerry Devine, who feels more strongly for her than she does for him. Meanwhile, Johnny agonises over his betrayal of his friend Tancred, a neighbour and former comrade in the IRA, who was subsequently murdered by Free State supporters; Johnny is terrified that the IRA will execute him as punishment for being an informant. Near the end of the act, one of Jack's relatives dies, and a solicitor, Mr Bentham, brings news that the Boyles have come into a large inheritance; Bentham notes aloud that the will names "John Boyle, [my] first cousin, of Dublin" as one of the beneficiaries. Overjoyed with the news, Jack vows to Juno to end his friendship with Joxer and change his ways.
A mere two days after receiving Mr Bentham's news, Jack has already begun flaunting his newfound wealth by purchasing a new suit, new furniture, a gramophone, and other luxuries on credit, in anticipation of receiving the inheritance. The Boyles throw a party and invite Bentham, who is courting Mary. Joxer is present, Jack having already forgotten his vow to break off contact with him, and Mrs Madigan, a neighbour to whom Jack owes money, shows up uninvited. During the party, Tancred's funeral procession passes the tenement, but the Boyles and their guests halt their carousing only when Tancred's grieving mother stops at their door. Juno goes out to offer support to Mrs Tancred who delivers a monologue mourning the loss of her son and praying for an end to the war, but Jack selfishly ignores her suffering.
Two months later, Mr Bentham abruptly ceases all contact with the family and abandons Mary, who, it is revealed, is secretly carrying his child out of wedlock. While Juno takes Mary to the doctor, the local tailor storms into the flat and repossesses Jack's suit, much to his chagrin. Soon after, Mrs Madigan arrives, demanding repayment of the loan she gave Jack; when he refuses to pay, she takes the gramophone as recompense. Joxer (who was present for both incidents, and did nothing to help) needles Jack about rumours that the inheritance is not forthcoming; this soon devolves into an argument during which Joxer openly mocks Jack's fortune as fraudulent, calling him "Jackie Boyle, Esquire: infernal rogue and damned liar." While Johnny upbraids his father for embarrassing the family, Juno returns alone and delivers the news of Mary's pregnancy. As Juno pleads with Jack to use the leftover money from the inheritance to move the family to a different city, he angrily reveals that they will receive nothing due to an error Bentham made while drafting the will (he failed to include the beneficiaries' names, referring to Jack only as "[my] first cousin"). As a result, numerous relations are claiming the inheritance, which is rapidly being eaten up by legal costs; to make matters worse, Bentham has apparently fled the country out of shame. Johnny berates his father for his shortsightedness and avarice. Unable to cope with the stress of the situation, Jack disowns Mary and retreats to the pub to drink with Joxer. Johnny convinces Juno to follow Jack and beg him to return. Mary returns home, and Johnny disowns her as well. Jerry Devine appears to patch things up with Mary, but he too renounces her when he learns of her pregnancy. As the last of Jack's fancy new furniture is being repossessed, several IRA men arrive and drag Johnny away; Juno later hears from Mrs Madigan that a body resembling Johnny's has been found on a country road, riddled with bullets. Juno decides that Jack will never take on his responsibilities as a father and breadwinner, so she leaves to make a better life for herself and Mary. She sends Mary to live with a relative and, before going to the police station to identify Johnny's body, delivers a monologue that echoes Mrs Tancred's in Act II. Some time later, Jack returns home with Joxer, both of them very drunk, unaware that his son is dead or that his wife and daughter have left him. After a brief conversation, Jack accidentally drops his last sixpence on the floor; he drunkenly mourns that "the whole world is in a terrible state o' chassis" before passing out. Joxer steals the coin and walks out, leaving the unconscious Jack on the floor of the empty flat, penniless and alone.