The process of adding students to courses is called Enrolment. This is different from adding users to the site, which is known as Authentication. There are various methods of enrolling students into courses, once they have logged in to Moodle.
A teacher can view, activate, add and remove the enrolment methods within their course from the Enrolment methods link accessed either from the gear menu in the nav drawer Participants link, or from the More link in the course gear menu (or in Course administration > Users in the Administration block if you are using a theme other than Boost). It may also be the case that the students are automatically enrolled into the course by an administrative process, and the teacher does not need to do anything.
Students enrol themselves
If Self enrolment is enabled then students can sign up to courses themselves. The teacher can restrict enrolment to those who have been given an Enrolment key and, if needed, a staff member may be given the Keyholder role to manage enrolment keys.
Student self-enrols into a course.
Teachers manually enrol students
If Manual enrolment is enabled (and it usually is) then teachers may add students to their course from the nav drawer Participants link by clicking 'Enrolled users' in the gear menu (or in Course administration > Users in the Administration block if you are using a theme other than Boost).
Allowing guests into a course
Guests may be allowed to view course contents, but not participate in them, if Guest access is enabled. To find out exactly what guests may and may not do in a course, see the page Guest role.