Befriend the faculty. Remember that faculty are people too, and in many cases they are interesting people. As a graduate student you are in a very different position from when you were an undergrad, particularly if you have an assistanceship and teach classes. This will allow the faculty to see you more as a colleague, even though you are still a student. Being friendly with the faculty will often net you extended deadlines, and more comfortable office visits.
Visit your professors, and ask them questions. Nothing is more helpful than a one on one session, and most professors are more than happy to meet with you during their office hours. If you have questions about the class material, an essay or even a conference paper, feel free to visit your prof during their office hours (they will usually be happy to have the company anyway).
Don't drink before class. You may have been able to get away with this during undergrad, but graduate classes are typically much smaller seminars.
Finish your work ahead of schedule. You cannot crunch a 25 page research project. It quite simply does not work.
Participate actively in conferences related to your area of study. You will always get more respect (and slack) from your graduate department if you actively present at conferences.
Act like you know what's going on (even when you don't). You will get eaten alive in most departments if it looks like you've lost your footing.
Get student loans. You may think that you can survive on the stipends provided for you by the university, but chances are you cannot. There is no shame in getting loans, and it will take off the edge of grad school if you don't have to count out your dimes to buy coffee.
Find time to exercise. Nothing is worse than feeling sedentary.