The student classes is determined in their class history. When you open a page from a previous month register, year or date, it will check the class history to find out what class the student was in.
When the student is in the waiting list or accepted status, you can assign the class from the Edit Student page
School > Classes > "Manage Students" (button under each class) and you can add the students one by one in to the class
To move a student to another class, go to School > Classes > "Move/Switch" button at the top > Move Students
Search the student name in the main search bar, on the results page click on "Class History" to modify the class history and add/remove them to a class
Where to find their full history:
Search the student name in the main search bar, on the results page click on "Class History"
Students > Manage Students > Actions (under each student) > Class History