showSaveDialog(Component parent)
private JFileChooser chooser;
[...]
//im Konstruktor
chooser = new JFileChooser(System.getProperty("user.home"));
[...]
//Aufruf des JFileChoosers
int returnVal = chooser.showSaveDialog(null);
if(returnVal == JFileChooser.APPROVE_OPTION) {
File file = chooser.getSelectedFile();
//hier dann deine Routine zum Speichern der Datei.
}