Develop a calendar that will help you compile all of your important dates. Test dates, paper due dates, quizzes, presentations, and personal engagements may all overlap, so it is important to know how these things fit together. Use your syllabi to figure out the dates. Don't simply put the dates down, but list the requirements for each. In addition, write the date that you intend to start studying for the various activities.
Work with your professors to figure out how to integrate the various obligations for your classes. When you take six classes, you'll inevitably have certain course requirements that overlap, and professors are usually willing to give you paper extensions or allow you to take tests early. Be sure to e-mail professors ahead of time and explain your situation.
Prioritize your classes in terms of difficulty and importance. Think about which classes will require more time and effort, and give them priority. Typically, upper level classes will require more work. If you are the type of student who frequently studies at the last minute, then you may want to study for your easy classes first, in order to get them out of the way and focus on your tougher requirements.
Ask for advice from other students who have braved a heavy course load. They can give you clues on how to prioritize your various courses.
Focus on one task at a time. Don't become stressed by constantly thinking about all the things you must do. Use your calendar and schedule to determine what you must do each day.