The Princeton Companion to Mathematics has a section Advice to a Young Mathematician, which seems available for free, where each of Atiyah, Bollobás, Connes, McDuff, and Sarnak give advice and most of it is of the form that it fits what is asked for in the question.
Terence Tao's blog contains various related information under Career Advice and On Writing; note that this is mostly different from the book 'Solving Mathematical Problems' mentioned in another answer, which he wrote more than two decades ago.
Cédric Villani has written a book Théorème Vivant that reads somewhat like a diary and generally feels very authentic, even including reproductions of some of his email correspondence. It might be of less practical value regarding finding advice or behavior to adopt, yet as far as conveying what it can be like "to live as a research mathematician" goes this is the best I know. The original is in French according to some rather recent information on his website it is also available in Italian, German, and Serbian while English, Romanian, Bulgarian, Japanesen and Korean versions are planned.
As a final note reading such things one shoud never forget that (as written by Connes in the text mentioned above) "each mathematician is a special case".