Get your information straight. Before meeting with your professor, organize your papers, quizzes, tests, notes and any extra credit work you did. Follow the professor's personal grading scale (usually handed out with the syllabus at the beginning of the course) and calculate whether he made a mistake.
List the points that support your argument. If the numbers all added up, then the issue is deeper than a simple mathematical error. Decide whether the professor's marginal notes are valid. Re-read the assignments or test questions to see if you misunderstood anything.
Be forthcoming about any personal issues that may have influenced a poor grade, including illness, depression or family problems. Some professors will consider extenuating circumstances and offer you a chance to raise your grade by proving you know the material.
Ask to re-do the work if a single assignment dropped your grade. Be willing to compromise with a 50% increase rather than holding out for a new grade.
Acknowledge any missing work. If you have missing assignments, quizzes or tests, don't make excuses. Ask if you can turn them in for partial credit.