Out of the box, enrollment is self-service. A signed-in student clicks Enroll on a course page or in the catalog and they’re in right away.
Courses with Enrollment Open switched off don’t accept new students.
An enroll button anywhere
You can put an enroll button anywhere on your site, including inside a lesson:
[nonprofit_lms_enroll_button course_id="123"]
It shows the right state on its own: enroll, continue, or enrollment closed. On a course’s own page it finds the course automatically. Anywhere else it needs the course_id, or it shows nothing.
With Pro you can also require approval or invite people. See Enrollment approvals and invitations.