How to Solve It starts with what you might call a summary. It covers two pages (printed sideways to form one large sheet) and it is, by far, the best known part of the book. This is both a good and a bad thing. On the good side, the sheet contains an extraordinary amount of useful ideas; on the bad side, the teachers who explain it often know little about Pólya's philosophy and treat the list as a kind of an algorithm for general problem solving.
Pólya disliked cookbook approaches and he believed that the search for a generalized approach to problem solving, while interesting and likely to yield useful insights, was a doomed effort. He certainly didn't mean for this list to be treated as an algorithm to be checked through. Here's how he puts it in the introduction:
Put another way, this is a list of things you can try when you're having difficulty solving a problem. They have an excellent track record over a wide range of situations and difficulty levels but they have to be applied with common sense in context and, even when used appropriately, they are meant to help you think through a problem, not to do your thinking for you.