How to close a GUI when I push a JButton?

See JFrame.setDefaultCloseOperation(DISPOSE_ON_CLOSE)¹. You might also use EXIT_ON_CLOSE, but it is better to explicitly clean up any running threads, then when the last GUI element becomes invisible, the EDT & JRE will end.

The 'button' to invoke this operation is already on a frame.

1. See this answer to How to best position Swing GUIs? for a demo. of the DISPOSE_ON_CLOSE functionality.
   
   The JRE will end after all 3 frames are closed by clicking the X button.

By using System.exit(0); you would close the entire process. Is that what you wanted or did you intend to close only the GUI window and allow the process to continue running?

The quickest, easiest and most robust way to simply close a JFrame or JPanel with the click of a JButton is to add an actionListener to the JButton which will execute the line of code below when the JButton is clicked:

this.dispose();

If you are using the NetBeans GUI designer, the easiest way to add this actionListener is to enter the GUI editor window and double click the JButton component. Doing this will automatically create an actionListener and actionEvent, which can be modified manually by you.

Add your button:

JButton close = new JButton("Close");

Add an ActionListener:

close.addActionListner(new CloseListener());

Add a class for the Listener implementing the ActionListener interface and override its main function:

private class CloseListener implements ActionListener{
    @Override
    public void actionPerformed(ActionEvent e) {
        //DO SOMETHING
        System.exit(0);
    }
}

This might be not the best way, but its a point to start. The class for example can be made public and not as a private class inside another one.