The play begins with Strepsiades suddenly sitting up in bed while his son, Pheidippides, remains blissfully asleep in the bed next to him. Strepsiades complains to the audience that he is too worried about household debts to get any sleep – his wife (the pampered product of an aristocratic clan) has encouraged their son's expensive interest in betting on horse races. Strepsiades, having thought up a plan to get out of debt, wakes the youth gently and pleads with him to do something for him. Pheidippides at first agrees to do as he is asked then changes his mind when he learns that his father wants to enroll him in The Thinkery, a school for wastrels and bums with which no self-respecting, athletic young man dares to be associated. Strepsiades explains that students of The Thinkery learn how to turn inferior arguments into winning arguments and this is the only way he can beat their aggrieved creditors in court. Pheidippides however will not be persuaded and Strepsiades decides to enroll himself in The Thinkery in spite of his advanced age.
There he meets a student who tells him about some of the recent discoveries made by Socrates, the head of The Thinkery, including a new unit of measurement for ascertaining the distance jumped by a flea (a flea's foot, created from a minuscule imprint in wax), the exact cause of the buzzing noise made by a gnat (its rear end resembles a trumpet) and a new use for a large pair of compasses (as a kind of fishing-hook for stealing cloaks from pegs over the gymnasium wall). Impressed, Strepsiades begs to be introduced to the man behind these discoveries. The wish is soon granted; Socrates appears overhead, wafted in a basket at the end of a rope, the better to observe the Sun and other meteorological phenomena. The philosopher descends and quickly begins the induction ceremony for the new elderly student, the highlight of which is a parade of the Clouds, the patron goddesses of thinkers and other layabouts. The Clouds arrive singing majestically of the regions whence they arose and of the land they have now come to visit, loveliest in all being Greece. Introduced to them as a new devotee, Strepsiades begs them to make him the best orator in Greece by a hundred miles. They reply with the promise of a brilliant future. Socrates leads him into the dingy Thinkery for his first lesson and The Clouds step forward to address the audience.
Putting aside their cloud-like costumes, The Chorus declares that this is the author's cleverest play and that it cost him the greatest effort. It reproaches the audience for the play's failure at the festival, where it was beaten by the works of inferior authors, and it praises the author for originality and for his courage in lampooning influential politicians such as Cleon. The Chorus then resumes its appearance as clouds, promising divine favours if the audience punishes Cleon for corruption and rebuking Athenians for messing about with the calendar, since this has put Athens out of step with the moon.
Socrates returns to the stage in a huff, protesting against the ineptitude of his new elderly student. He summons Strepsiades outside and attempts further lessons, including a form of meditative incubation in which the old man lies under a blanket while thoughts are supposed to arise in his mind naturally. The incubation results in Strepsiades using the blanket to masturbate; finally, Socrates refuses to have anything more to do with him. The Clouds advise Strepsiades to find someone younger to do the learning for him. His son, Pheidippides, subsequently yields to threats by Strepsiades and reluctantly returns with him to the Thinkery, where they encounter the personified arguments Superior (Right) and Inferior (Wrong), associates of Socrates. Superior Argument and Inferior Argument debate with each other over which of them can offer the best education. Superior Argument sides with Justice and the gods, offering to prepare Pheidippides for an earnest life of discipline, typical of men who respect the old ways; Inferior Argument, denying the existence of Justice, offers to prepare him for a life of ease and pleasure, typical of men who know how to talk their way out of trouble. At the end of the debate, a quick survey of the audience reveals that buggers – people schooled by Inferior Arguments – have got into the most powerful positions in Athens. Superior Argument accepts his inevitable defeat, Inferior Argument leads Pheidippides into the Thinkery for a life-changing education and Strepsiades goes home happy. The Clouds step forward to address the audience a second time, demanding to be awarded first place in the festival competition, in return for which they promise good rains – otherwise they will destroy crops, smash roofs, and spoil weddings.
The story resumes with Strepsiades returning to The Thinkery to fetch his son. A new Pheidippides emerges, startlingly transformed into the pale intellectual man that he had once feared to become. Rejoicing in the prospect of talking their way out of financial trouble, Strepsiades leads the youth home for celebrations, just moments before the first of their aggrieved creditors arrives with a witness to summon him to court. Strepsiades comes back on stage, confronts the creditor and dismisses him contemptuously. A second creditor arrives and receives the same treatment before Strepsiades returns indoors to continue the celebrations. The Clouds sing ominously of a looming debacle and Strepsiades again comes back on stage, now in distress, complaining of a beating that his new son has just given him in a dispute over the celebrations. Pheidippides emerges coolly and insolently debates with his father a father's right to beat his son and a son's right to beat his father. He ends by threatening to beat his mother also, whereupon Strepsiades flies into a rage against The Thinkery, blaming Socrates for his latest troubles. He leads his slaves, armed with torches and mattocks, in a frenzied attack on the disreputable school. The alarmed students are pursued offstage and the Chorus, with nothing to celebrate, quietly departs.
