I first encountered R.J. Hollingdale's "Nietzsche: The Man and his Philosophy" in a class on Nietzsche in college, and I'm pleased to say that it still very much holds up on a second reading.
Hollingdale not only provides a very accessible introduction to the general thrust of Nietzsche's philosophy (especially his three main ideas: the Superman, the will to power, and the eternal recurrence); he also paints a compelling picture with regard to the intellectual climate of the late nineteenth century, and situates Nietzsche's philosophy as a response to certain trends of that period, such as the rise in popularity of Darwinism and Schopenhauerean pessimism. Furthermore, the writing is crisp and easy to follow: a testament to this would be the genuine feeling that, as a reader, I felt for Nietzsche as he progressed deeper into his solitary and excruciatingly painful existence, climaxing in an eventual descent into insanity from 1889-1900.
In my opinion, this book is a masterstroke in content as well as its form. I believe that Hollingdale's biography is required reading for anyone, layperson or otherwise, who wishes to understand the German philosopher's life and thought in their proper historical context.