I have collected below some resources for aspiring and young mathematicians:
Advice to a Young Mathematician
Career advice from Terrence Tao
NSF CAREER Proposal Writing Tips
A particularly insightful comment from Prof. Michael Atiyah is "one could say that all the really creative aspects of mathematical research precede the proof stage."
Prospective and current UCSD Math graduate students should consult the UCSD Mathematics Graduate Handbook, which is full of useful practical advice.