Don't worry - they don't need one!
We realize that many students may not have an email address, so for Handouts all students need to register is a unique username. This can be anything that has not already been taken by another user - maybe each student has a unique class or student ID, for example. Or you could use a mix of their first and last names, e.g. for the student Jane Smith, the username could be janes, jsmith or janesmith. The possibilities are endless! Just make sure it's something easy to remember and get them to keep a record of it some place safe :-)