In "The Fat Man and the Sea", a mini-side plot involves Brian saying that he wants to start writing a book. The entire episode, he brags about how brilliant of a writer he's going to be, while also procrastinating and not writing a single word down.
In "Brian the Bachelor", Stewie asks Brian how he's coming on the novel he's been working on, and if he's been working on it the whole time, and if some friends become enemies, some enemies become friends, or if at the end his main character is richer from the experience. It is then mentioned that he has been working on the novel for three years.
It wasn't mentioned again until "Movin' Out (Brian's Song)", where he comes up with the name "Faster Than the Speed of Love" for his novel, which Lois mocks him about, saying she thinks that's the worst title she's ever heard. He then tells her what the story is about, and we find out that the plot line is essentially a rip off of the Iron Eagle movie series, even though he claims he's never seen the movies. His main character, a boy, has got to gather all these old World War II pilots to help him rescue his father, which is the third movie.
It is then mentioned again in "Baby Not On Board", when Stewie replaced every single usage of the word "and" with the word "fart". He thought it was amusing at first but got bored of the joke extremely quickly.
Faster Than the Speed of Love is finally published in "420". Carter Pewterschmidt publishes two million copies of "Faster Than the Speed of Love" and gets Oprah Winfrey to endorse it, and would be released if Brian sells out and does a public musical performance to make marijuana illegal once again. With Stewie's "support", he agrees to do so. It was later revealed by Tom Tucker in a news broadcast that it set a record for the "worst selling novel of all time", not selling a single copy as it was universally panned by literary critics.
In "Dog Gone", Brian's novel gets awarded for "Special Literary Excellence" at Pizza Parlor, but it turns out to be given by a group of mentally disabled people.
In "Brian Writes a Bestseller", Brian receives 300 boxes of the many copies of his novel returned to him, since his publisher noted how the novel failed to make one sale. This convinces Brian that he's not meant to be a writer and give up. The failed novel's paper shreds were used to pack the boxes of returned novels, as well as other items. This was the final straw, urging Brian to finally give up on hope with the book.