Some would argue there is no better book you can read than Graduate Study for the 21st Century. Many of my professors recommended it for anyone going into grad school for the humanities. Beware though—it is extremely honest.
The best book I have yet seen that actually focuses on what graduate school is like and what it takes to succeed (as opposed to focusing more on the application process) is Gregory Semenza's <i>Graduate Study in the Twenty-First Century</i>. It's focused primarily on the Humanities but I suspect it would be generally useful for STEM prospectives as well. If I had to recommend one book to someone considering graduate school or just wanting to know what it is like to be a graduate student, this is the one.
http://www.amazon.com/Graduate-Study-Twenty-First-Century-Humanities/dp/0230100333