This is a bit of a weird one as they aren't really collectables.
At the start of the game, John will have a choice of three books to read to his mum (The Bible, a technical guide about nuclear bomb procedures and a novel of Treasure Island). Pick one of these and continue on.
When doing the routine, you'll come back to John's mum and get the chance to read to her again. Pick one of the books you haven't read yet and continue on.
The third and final time John reads to his mum, he seems to automatically pick the book you didn't choose the other two times (Treasure Island for me) and then the achievement unlocks soon after. For the record, the order I read them in was The Bible, the guide and then John automatically read Treasure Island to finish.
EDIT: It appears that Treasure Island might be always read third no matter what you do. To be safe, do my order to guarantee all three books.