Here is the relevant code to your problem (next time you should add relevant code to your post instead of just put a link to some other site):
public class TTTGraphics2P extends JFrame {
    ...
    private DrawCanvas canvas; // Drawing canvas (JPanel) for the game board
    private JLabel statusBar;  // Status Bar
    public TTTGraphics2P() {
        ...
        statusBar = new JLabel("  ");
        statusBar.setFont(new Font(Font.DIALOG_INPUT, Font.BOLD, 15));
        statusBar.setBorder(BorderFactory.createEmptyBorder(2, 5, 4, 5));
        Container cp = getContentPane();
        cp.setLayout(new BorderLayout());
        cp.add(canvas, BorderLayout.CENTER);
        cp.add(statusBar, BorderLayout.PAGE_END); // same as SOUTH
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        pack();  // pack all the components in this JFrame
        setTitle("Tic Tac Toe");
        setVisible(true);  // show this JFrame
    }
    ...
}
I'm having trouble with adding text relative to the position of other
  elements. I have tried creating another container but it's not
  working. I would like to place a footer of text either below the
  "statusBar" or above it.
Don't know what have you tried but you can follow a Nested Layout approach and wrap two (or many as needed) components into a panel and add this one at content pane's south position. Something like this:
    ...
    statusBar = new JLabel("  ");
    JLabel someOtherLabel = new JLabel("Some other label!");
    JPanel southPanel = new JPanel(new GridBagLayout());
    GridBagConstraints constraints = new GridBagConstraints();
    constraints.weightx = 1;
    constraints.anchor = GridBagConstraints.WEST;
    constraints.fill = GridBagConstraints.HORIZONTAL;
    constraints.insets = new Insets(8,8,8,8);
    southPanel.add(statusBar, constraints);
    constraints.gridy = 1;
    southPanel.add(someOtherLabel, constraints);
    Container cp = getContentPane();
    cp.setLayout(new BorderLayout()); // default layout manager is actually BorderLayout
    cp.add(canvas, BorderLayout.CENTER);
    cp.add(southPanel, BorderLayout.SOUTH);
    ...
Note: the example makes use of GridBagLayout but might find a more suitable layout manager based on your needs.
Suggested reading
Take a look to Lesson: Laying Out Components Within a Container