To add a course that is full, keep looking for an opening in the course during the first week of the semester until the add deadline listed on the academic calendar.
Talk with the instructor of the class. The instructor could sign a drop/add form to add you to the course. Submit the completed form to the Registrar's office. If the fire code limit of people for the classroom has been exceeded, the registrar's office would not be able to add you to the course.
If offered, use the waitlist for the course.