Read what I wrote for undergraduate students. Scientific networking becomes more important during graduate school, and should not be underestimated. You obviously spend most of your time and creative energy doing research. It still will be helpful (for both of these goals) to find out stories about other scientists.
The main new things that you are asked to learn in graduate school are:
Taking more responsibility for yourself and your career. In addition to effectively managing time, you should also learn more about how universities and academic careers work (e.g. by reading the pages on this website carefully, including the ones for postdocs, but also by asking more of your senior colleagues about it), and develop professional habits of interaction (see the networking page; do not underestimate this part). Generally with networking, I recommend you make it your goal that every professor in your home department should know you by name and roughly what your work is about, by the time you graduate. This is not that hard, but it does require consistent deliberate investment over the years (at dept. receptions, seminars, and so on). It also requires genuinely caring about what their research is about.
One part of finding out more about university organization is finding out about the details of how your graduate program works and is administered. You must read your graduate student handbook, given out by your program, and plan to stick to all the requirements to the letter. Discuss deviations with your advisor ideally before they are unavoidable (EEB, EIS handbooks are most relevant for students in my lab). Also find out who at the university really decides what about the requirements for graduate students, how students are funded, etc. Ask your advisor, other faculty, the grad program coordinator.
How to pick research projects and bring them to a published outcome. This is of course what doing research is about.
The broader picture that your research fits into. You should be spending a lot of time reading. You need to master a field of literature by the end of your PhD, in the sense of knowing the paradigms, where the holes are, the commonly studied organisms, the well-known authors and seminal papers as well as who is working in your area right now. You need to know several angles of how your research is relevant to different communities in science (e.g. applied entomology, robotics, complex systems science, evolutionary theory) and outside science (your mom, your congressman, your neighbor, your university administrator).
And the end, you get to apply for postdoc positions if you are planning to stay in academia. I recommend identifying a short list of 2-5 professors you'd like to work with by about 1 year before you graduate, and writing to them then.
Some other websites about graduate school:
How to succeed in graduate school by Marie desJardins
Classic PhD comic with a grain of truth by Jorge Cham (The grain of truth is that your motivation or satisfaction will fluctuate widely because of the long delayed gratification in most research projects. Do NOT be silent about this - discuss with your lab mates, other students, and your advisor to develop stragtegies for progress and to put your work/output in perspective.)
Other specific advice:
How to prepare for your 'prelims' = 'comps' = 'comprehensive examination'