Many young, and not so young, mathematicians struggle with how to spend their time. Perhaps this is due to the 90%-10% rule for mathematical insight: 90 pages of work yield only 10 pages of useful ideas. A venerable mathematician once described his career to me as constantly stumbling around in the dark. Of course, this struggle is largely personal...perhaps it is an evolutionary struggle to find one's own way to find something relevant to contribute to mathematics as literature. Such an evolutionary struggle necessitates the artist's turmoil and requires an acknowledgement of "l'importance d'être seul". Even when I have successfully done some reasonable mathematics, it behooves me to look for a more efficient way to proceed. This sort of searching turns up various nuggets of advice on how to do mathematics, like the following (paraphrased) ones:
Read a paper of a master for a year, and you will get something- advice given to young mathematicians by Israel Gelfand at Harvard during his 90th birthday conference on the unity of mathematics.
Try to imagine a proof, no matter how vague-Gowers's online essay on the philosophy of mathematics and our relationship to formalism
I try to colorize it in my mind, to try to see what it's really getting at, rather than simply what it says-Thurston's online response to Ashley Reiter on reading mathematics.
Also recall Grothendieck's images of a softening nut and the rising sea...online interviews/documents with suggestions of Atiyah, Singer, Connes, Gromov...
There are many other such nuggets, many of which can be found on posts on this site. These all provide very inspiring images, but I would like to be more blunt:
What is your method? How do you go about doing mathematics on a day to day basis?