It's pretty straight forward.
Take the text from the textArea:
String theText = myTextArea.getText();
Put in a label:
myLabel.setText( theText );
In a button listener:
myButton.addActionListener( new ActionListener() {
@override public actionPerformed( ActionEvent event )
{
String theText = myTextArea.getText();
myLabel.setText( theText );
}
} );
EDIT
Looking at your edit, your problem is that you add a component to your frame without revalidating (JFrame#revalidate()
) it.