My answer is quite philosophical and the books concerned with guided discovery, which I read, are less concrete than proposed by the others:
- George Polya, “Mathematical discovery: on understanding, learning and teaching”
- Henri Poincaré, “Mathematical Creation”.
- Imre Lakatos, “Proofs and refutations. The Logic of Matematical Discovery”
- Jacques Hadamard, “An essay on The Psychology of Invention in the Mathematical Field”
- Louis Mordell, “Reflections of a mathematician”
- Karl Popper, “The Logic of Scientific Discovery”
- Simon Singh, “Fermat's last theorem” (how they did it)
I hope that the titles of the books are descriptive. I wish to present short abstracts for these books, but it is hard to me. These guys are famous, and I can say to a seeker: Cast a glance at the book. It you’ll found it good for you it’ll be OK. If not – this also be OK, there are a lot of other books in the world. :-)
Also some useful advices can be found from this page by Terence Tao, who is a Fields Prize Winner.
Instead of the abstracts I can share with a reader my general point of view on the usage of such books. Thus a reader not interested in ideology can finish read my answer here.
I believe that principles of scientific discovery are objective, because a method which regularly leads to a success, which was successful not only for a first discovery, but which will lead us to the future discoveries, have to be based on objective, universal foundations, such as gravitation laws or mathematical arguments. From this point of view history of science is a concrete illustration of general principles. Therefore I believe that a right way for a scientist is not to deal independently, but to deal good. Leonardo da Vinci said: “There are three classes of people: those who see, those who see when they are shown, those who do not see”. So I want to believe that an urge to independent thinking results from poverty, therefore I wish that a seeker could say, like Nietzsche's Zarathustra: “I am not poor enough for that”. :-) I think that a right way is a way of masters, because both masterity and masters are winners in concurrent struggle of alternatives, they endure selection and trials (by life), proved its effectiveness, success. Therefore way of masters is in some sense a natural way. Life stands problems before us (due to nature of the world) and we strive to solve them (due to our nature). Thus a masters way is about deep acquirement and use of masters’ (effective) methods (strategies, doctrines, theories, schemes, modes of thought and act, moods, at last), form and development of intuition, improvement of masterity. Then great masters books stands as lighthouses along a way of a seeker, who wish to follow masters way, do as they do.