Start forming relationships with your potential committee early. Doing well in your coursework is necessary, but building relationships with professors early will simplify the committee process, and help with your future dissertation research and editing.
Write your course papers using highly reliable sources. You can get feedback from your professors and then submit your term papers to journals for publication. The more you write, the better you'll write your dissertation. A couple of published papers in peer-reviewed journals will help build your CV while being a student.
Study almost to the excess for your comprehensive exams. Most Ph.D. programs only allow you to take your exams twice. Comprehensive exams are graded by a small panel and sometimes by your supervisory committee. They normally cover your major and minor area, and your theoretical knowledge.
The dissertation is an independent research study that should contribute to the body of knowledge in your academic discipline. Your supervisory committee and advisor will expect you to do the legwork and turn in edited versions of your work, not just rough drafts.
Set up a time line on how you plan to research and write your dissertation, and share this with your supervisory committee or adviser. Be realistic--your time line won't impress the committee if you finish within miraculously short time frames and then turn in shoddy work. Be honest with your committee if you fall behind, and then communicate with them the steps you'll take to catch up.
Prepare for your dissertation defense by practicing in front of the mirror, in front of family and friends, and in front of your adviser or a colleague. It's useful to prepare a list of potential questions and responses, and have your friends and adviser ask them. Confidence is important.