The story begins by introducing George, Harris, Jerome (always referred to as "J."), and Jerome's dog, a fox terrier called Montmorency. The men are spending an evening in J.'s room, smoking and discussing illnesses from which they fancy they suffer. They conclude that they are all suffering from "overwork" and need a holiday. A stay in the country and a sea trip are both considered. The country stay is rejected because Harris claims that it would be dull, the sea-trip after J. describes bad experiences of his brother-in-law and a friend on sea trips. The three eventually decide on a boating holiday up the River Thames, from Kingston upon Thames to Oxford, during which they will camp, notwithstanding more of J.'s anecdotes about previous mishaps with tents and camping stoves.
They set off the following Saturday. George must go to work that day, so J. and Harris make their way to Kingston by train. They cannot find the right train at Waterloo Station (the station's confusing layout was a well-known theme of Victorian comedy) so they bribe a train driver to take his train to Kingston, where they collect the hired boat and start the journey. They meet George further up river at Weybridge.
The remainder of the story describes their river journey and the incidents that occur. The book's original purpose as a guidebook is apparent as J., the narrator, describes passing landmarks and villages such as Hampton Court Palace, Hampton Church, Magna Carta Island and Monkey Island, and muses on historical associations of these places. However, he frequently digresses into humorous anecdotes that range from the unreliability of barometers for weather forecasting to the difficulties encountered when learning to play the Scottish bagpipes. The most frequent topics of J.'s anecdotes are river pastimes such as fishing and boating and the difficulties they present to the inexperienced and unwary and to the three men on previous boating trips.
The book includes classic comedy set pieces, such as the story of two drunken men who slide into the same bed in the dark, the Plaster of Paris trout in chapter 17, and the "Irish stew" in chapter 14 – made by mixing most of the leftovers in the party's food hamper:
I forget the other ingredients, but I know nothing was wasted; and I remember that, towards the end, Montmorency, who had evinced great interest in the proceedings throughout, strolled away with an earnest and thoughtful air, reappearing, a few minutes afterwards, with a dead water-rat in his mouth, which he evidently wished to present as his contribution to the dinner; whether in a sarcastic spirit, or with a genuine desire to assist, I cannot say.
— Chapter 16
Other memorable sections include chapter 3's description of the author's Uncle Podger creating chaos while hanging a picture, and chapter 4's discussion of "Advantages of cheese as a travelling companion".

Question: What is Montmorency's relationship to Jerome?
Answer: Montmorency is Jerome's dog.
Alternative answer: He is Jerome's fox terrier.