Each course can have a number of students that follow it. To enroll student in the course, go to the course page and select the Users sub-page in the left panel. You will now see a list of users involved in the course. This contains the course administrator(s), possibly editors and checkers, and the students. Click on Add Users to add students (and other users) to the course.
Once students are added, as long as a course is "open", the students can make the assignments in the course. When the course is over you might want to archive the course. although this is not strictly necessary (as long as the course has an end date). At any moment the teacher can inspect reports for the progress of the students and make assessments.