It's delightful to see this book is still in bookstores after 60 years, and I can still remember how much fun it was to read it 30 years ago. I came across it recently in a local bookstore, and after poring over it again, I was inspired to write a little review about it.
The most important thing about the book is Polya's little heuristic method for breaking down math problems and guiding you thru the process of solving them. Try to visualize the problem as a whole. Diagram it at first, even if you don't have all the details. Just initially try to get the most important parts of the problem down. Then try to get some sense of the relationship of the parts to the whole. Then tackle each of the component parts. If you get stuck, ask yourself if you could approach it another way, what could be missing, and so on. To this end, the questions at the back of the book are worth their weight in gold.
Polya's little heuristic and methods book is a timeless classic. This and Lancelot Hogben's "Mathematics for the Millions" have done more good for suffering math students than all the the dry textbooks put together that really don't teach you "how to solve it."