Hard problems solving tricks

I think that a typical situation of a working mathematician is described by Nicholas Bourbaki, who said that “the mathematician does not work like a machine, nor as the workingman on a moving belt; we can not over-emphasize the fundamental role played in his research by a special intuition, which is not the popular sense-intuition, but rather a kind of direct divination (ahead of all reasoning) of the normal behavior, which he seems to have the right to expect of mathematical beings, with whom a long acquintance has made him as familiar as with the beings of the real world”.

This vision should be helpful to solve the most of usual problems.

The base of a general method of hard problem solving is sketched in a book “Mathematical discovery: on understanding, learning and teaching” by George Polya.

Should I just learn them "on the job"?

I think this is a usual way.

Why the origin of these tricks isn't explained?

I think there is no need for that. Also there is no need to memorize tons of tricks, because they come naturally, when you have knowledge. I think a trick usually emerges while thinking on the problem. I recommend Chapters 10–12 of Polya’s book for details.

how could I find these tricks myself and make them natural?

I can add to the above a few finding hints. Try to see a problem from different points of view, search familiar elements in the problem. Return to the problem time after time.

Should I be worried (as a student in mathematics) if I don't see them?

I think that although there can be specific mind problems blocking trick vision, usually a student in mathematics should not be worried about that. 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”. A problem solver sometimes sees some tricks. More advanced see more, less advanced see less. But trick vision often requires a luck and even a very good problem solver can miss a simple trick.

Is there a book that lists some of them

I think a source for the tricks should be not a list but a general mathematical knowledge. Remark that “Mathematical quickies” by Charles Trigg is a collection of problems with tricky solutions.