Repeat the class that you failed or withdrew from. If you do not believe that you can do better than you did originally, then you may not have much of a case for the class's removal. You must be able to demonstrate that you did not fail because of an inability to pass, and retaking the course will help with this.
Confront your college adviser and, together, assess why you did poorly or withdrew from a course. To petition for grade eradication, your answer to why you didn't do well originally will greatly impact your success at having the grade removed.
Speak with the Dean of Students once you have your adviser's blessing. This may include a formal written letter explaining the exact reasons behind your failed grade and your attempts to correct it by retaking the course. The Dean may then have the letter reviewed by the head of the department of that course for an appropriate assessment.