The students need to be given access to a course before they are allowed to use it. The users need to be assigned a role within a course before they are allowed to do anything. They can be assigned the role automatically by self-enrolling, or manually using the Assign roles link in the course administration block (see Chapter 6 Roles Management).
The actual enrolment of students does not require administrator rights, and is a task which should be performed by teachers. The role of the administrator is to set up the available site-wide enrolment mechanisms and they are covered next.
You access the course enrolments configuration page via Courses | Enrolments in the Site Administration block. Each supported enrolment mechanism is represented by an enrolment plug-in that can be enabled and configured separately.