Well, there are a couple of ways to access variables from other classes. This really isn't GUI specific as you would do this in almost any Java program.
The first way, and probably the prefered way, is to create your class with getter methods for the values you need. Kind of like a Javabean, but as this Class probably does more than store data..
Then in your other class you would simply do something like
A less coded way of doing the same thing would be to store all your answers in some sort of a Collection class instead of individual Strings.
The other way would be to declare all your variables public and just access them like completedQuestionaire.answer1;
And yet another way is to declare all the variables public static and then you don't even need an instance of your CompletedQuestionaire class. All you have to do is specify the class name and the variable like CompletedQuestionaire.answer1;
Ok, so now that I have throughouly confused you...If you want to try one of those options out and then when you are having problems with the code, you can post the code here and we can help you better.