1. Make a good faith effort to complete assignments on time, but don't be scared to ask for extensions. Don't drag assignments out longer than they need to be. When the next semester starts, it's time to start on the next semester. That said, if a week or two will really make the difference as to whether your paper's worth reading, most professors would rather read something worthwhile later instead of crap by the deadline. Grad school's not undergrad. You shouldn't just try to get by. Note: in every department there are exceptions to the rule, ask your fellow grad students to find out who the exceptions are. Which leads me to..
2. During the first semester of graduate school, I really think it's important to take time to socialize, particularly with the people in your class and the class above you. You're going to be dealing with these people for 6ish years of your life, and we've got to live a little to in grad school.. right? Investing a little time up front to build relationships helps to make the whole experience better. Plus, if I'm right you've got the perfect excuse to hit up happy hour after seminars.
Any other sage words of wisdom for the newcomers?
-- Second Suitor