This book goes into some detail about how Gerrold came to write the titular episode, and includes several drafts as well as the final script, each annotated with information about how and why some of the earlier concepts were changed for the final script. In addition to describing the writing process, Gerrold gives a bit of information about how the props were made and how shooting went, and finally reflects on the impact the episode has had, both on him and others. He concludes the book with an anecdote about sending a spare tribble to a hospital to encourage a girl, paralyzed by meningitis, in her recovery.
This isn't the first time I've mentioned this book–I noted it last year, when I wrote about Gerrold's The World of Star Trek (published simultaneously), but I've only recently acquired a copy. Was it worth the wait?
Not really. It's well written, of course, and amusing enough to read, but by the time I got through the final draft of "The Trouble With Tribbles", I was pretty well sick of the story. Whitfield's The Making of Star Trek goes into more interesting detail about the production aspects, and Gerrold's own The World of Star Trek is a more interesting look at the writing. The form of the book is basically autobiographical, but it's rather scant of details. There's a little talk at the beginning on how Gerrold has always been a fan of science fiction, and a few more anecdotes scattered throughout, but otherwise the focus is very much on the revision of the script.
My suggestion: unless you're a particularly big fan of "The Trouble With Tribbles", read The World of Star Trek, instead.