Look at your professor's feedback on papers. Make a list of the weaknesses noted on the paper. Track your mistakes for each teacher to see if you are consistently making the same errors.
Pick up a basic grammar workbook. Brush up on your writing skills by working on the assignments during the semester. Understanding the basic rules of grammar can help you improve your syntax and help to eliminate basic usage errors.
Meet with your professor during office hours to review previous papers. Get one-on-one instruction instead of relying solely on comments. Some teachers do not have the time to provide extensive written feedback, and an in-person conference can give you more insight into areas in which you can improve.
Write all papers in advance. This means writing a draft a few days before the paper is due. Set the paper aside for a day or so, and then bring it out to review. As you read through it, refer to your checklist of common mistakes. Revise and edit as many times as needed, and do not forget to proofread a final time for spelling errors.
Have a friend proofread your papers as well. This will give you another opinion, which will help you see if you are getting your point across. It can be very difficult to proofread your own work, especially if you have not written the paper far enough in advance and are working under a tight deadline.
Write as much as possible. Ask professors for additional writing topics to work on between assignments. Ask your professor to review your work, if possible.