Eliminating global variables in GUI program
A thing I like to do is instead of using four different JButtons is use an array of four JButtons that is initialized in the same method that you build the JPanel this would remove the need to have them as global variables. Also instead of using two different methods to create your JPanels just use one that returns a JPanel as you can see you can remove the JButtons and the two JPanels this way:

public JPanel buildOperatorPanel()
{
    JPanel operatorPanel = new JPanel();
    operatorPanel.setLayout(new FlowLayout());

    JButton[] buttons = new JButton[4];//the array of JButtons
    String[] buttonNames = {"+", "-", "/", "*"};//the names to be displayed on the JButtons
    for(int i = 0; i &lt; buttons.length; i++)
    {
        buttons[i] = new JButton(buttonNames[i]);
        //buttons[i].addActionListener(yourActionListener)//for whenever you add event handling
        operatorPanel.add(buttons[i]);
    }
    return operatorPanel;
}


Another thing I could suggest is instead of named reference variables for your JLabels use anonymous objects so for operationLabel (this is only assuming your not going to use the JLabels later):

add(new JLabel("YOU HAVE PERFORMED SOME OPERATION", SwingConstants.CENTER), BorderLayout.SOUTH);


However I am going to suggest that you move the JTextFields to global variables. Based on what I'm assuming you have to do with this calculator you are going to want the JTextFields to be accessible to everything.
Here is my revision of your code:

import java.awt.BorderLayout;
import java.awt.FlowLayout;
import java.awt.GridLayout;
import javax.swing.JButton;
import javax.swing.JFrame;
import javax.swing.JLabel;
import javax.swing.JPanel;
import javax.swing.JTextField;
import javax.swing.SwingConstants;

public final class Calculator extends JFrame
{
    private JTextField operandOneText;//these get initialized in buildOperandPanel() method which is called in the constructor
    private JTextField operandTwoText;
    private JTextField answerText;

    //constructor to initialise the frame and add components into it
    public Calculator()
    {
        super("Clancy's Calculator");
        setLayout(new BorderLayout(5, 10));
        setResizable(false);
        setSize(370, 200);
        setDefaultCloseOperation(EXIT_ON_CLOSE);
        setLocationRelativeTo(null);
        setVisible(true);

        add(buildOperatorPanel(), BorderLayout.NORTH);
        add(buildOperandPanel(), BorderLayout.CENTER);
        add(new JLabel("YOU HAVE PERFORMED SOME OPERATION", SwingConstants.CENTER), BorderLayout.SOUTH);

        pack();
    }

    //method builds and returns operatorPanel
    public JPanel buildOperatorPanel()
    {
        JPanel operatorPanel = new JPanel();//JPanels are FlowLayout by default

        JButton[] buttons = new JButton[4];
        String[] buttonNames = {"+", "-", "/", "*"};
        for(int i = 0; i &lt; buttons.length; i++)
        {
            buttons[i] = new JButton(buttonNames[i]);//the array of JButtons
            //buttons[i].addActionListener(yourActionListener)//for whenever you add event handling
            operatorPanel.add(buttons[i]);
        }
        return operatorPanel;
    }

    //method builds and returns operandPanel
    public JPanel buildOperandPanel()
    {
        JPanel operandPanel = new JPanel();
        operandPanel.setLayout(new GridLayout(3, 2, 5, 5));

        //Initialize TEXT FIELDS
        operandOneText = new JTextField();  //retrieves one operand
        operandTwoText = new JTextField();  //retrieves another operand
        answerText = new JTextField();    //displays answer

        answerText.setEditable(false);  //ensure the answer field is not editable

        operandPanel.add(new JLabel("Enter the first Operand: "));
        operandPanel.add(operandOneText);
        operandPanel.add(new JLabel("Enter the second Operand: "));
        operandPanel.add(operandTwoText);
        operandPanel.add(new JLabel("ANSWER: "));
        operandPanel.add(answerText);

        return operandPanel;
    }

    /** main method */
    public static void main(String[] args)
    {
        new Calculator();
    }
}