Howdy. I see you got some code going for the "done" button. Looks good so far.
First
you should remember that your "action listener" class (DoneButtonListener) should have access to the JTextFields variables assignNameTF, monthDueTF, dayNumberDueTF, which I assume is outside your action listener (which is fine). If the DoneButtonListener class does NOT have access to those text fields ... make them instance variables rather than local variables.
Just curious what is the "validate()" and "repaint()" methods? If repaint, you mean refresh the screen then those textfield.setText("") lines are not needed. Put those in the repaint method. As for validate, what needs validating?
Also just a side note, if your form is a month/day calendar kind of input, you may want to use a JComboBox for the month and day instead, so that people wouldn't input wrong values. And your listener is guaranteed to get the correct values (given it is selected eg not null).