The html page showing the checkboxes would evolve from a join as you say.
You want student id and student name in order to output your check boxes eg:
<input type=checkbox name=students value=student /> Barbara Streisand <br />
SELECT s.student_id as id, s.student_name as name
FROM students_table as s
LEFT JOIN course_registrations_table as r
ON s.students_id = r.students_id
ORDER BY students_name
Where my student_id fields are obviously the ones you want to join on. As you provided no db schema, I guessed some column names to illustrate.