Hello tmcdiarmid:

From the main page, click students at the top. 

Once in the student menu, select the button to the right of the row with the students name. Now, at the top, click add to class. Add student to the section you would like them to join.

Only remove student from the other section, after you gather all of their scores that you may need because once you remove a student unfortunately you cannot track them.

Thanks for that response, but it didn't bring his work to the new class =(

That is why I mentioned to gather all of the scores you may need before you delete them from the other class. It will not carry over. If you did not delete the student yet, you can keep him there and when you assign new work to his former class you can just uncheck him so he doesn't get them but his past work will still be there.