I believe that one of the keys to success in terms of graduate studies and beyond is to be passionate about your work; this makes the dedication required to do well come that much easier.
My advisor was more like my mentor. He is very open, honest and helpful, which made me very comfortable to express my ideas and also to discuss different issues concerning my academic life.
There was a great graduate student community in my home department of Integrative Biology. As a group, we organized events ranging from salsa lessons and weekly communal meals, to wilderness retreats and a 'March Mammal Madness Bracket' pool.
I would encourage all prospective graduate students to research their program of interest and speak directly to faculty prior to applying as this can ensure that your research goals align with your prospective advisor/program of choice.
Find what interests you. Many other grad students are much younger than I am and will be entering a life's career following completion of their studies. Looking back, I think it's important to pursue your passion and let the career, money, etc., come from that. During studies, stay on top of things. At the same time, don't neglect other outlets, pursuits, interests: things have a way of connecting in unexpected ways.
Choose a supervisor who makes you excited about your project. There will be times when your project does not go as planned and reminders of that enthusiasm and why you are doing the work are crucial to continuing through the hurtles.