[hardwired]

For more on these kind of things see Trail: Creating a GUI with JFC/Swing.

Code:

import java.awt.*;
import java.awt.event.*;
import javax.swing.*;

public class GettingText implements ActionListener {
    JTextField hi = new JTextField(12);
    JTextField lo = new JTextField(12);
    JPanel panel;

    public void actionPerformed(ActionEvent e) {
        String hiText = hi.getText();
        String loText = lo.getText();
        boolean equal = hiText.equals(loText);
        int compare = hiText.compareTo(loText); // see String api
        System.out.printf("hiText = %s  loText = %s  " +
                          "equal = %b  compare = %d%n",
                           hiText, loText, equal, compare);
        CardLayout cards = (CardLayout)panel.getLayout();
        cards.next(panel);
        // or
//        cards.show(panel, "blue");
    }

    private JPanel getContent() {
        CardLayout cards = new CardLayout();
        panel = new JPanel(cards);
        panel.add("data", getComponentPanel());
        panel.add("blue", getBluePanel());
        return panel;
    }

    private JPanel getComponentPanel() {
        JButton button = new JButton("jump");
        button.addActionListener(this);
        // Optionally, you can also add the ActionListener
        // to the two textFields which will generate an
        // ActionEvent when you press the enter/return key.
        hi.addActionListener(this);
        lo.addActionListener(this);
        JPanel panel = new JPanel(new GridBagLayout());
        GridBagConstraints gbc = new GridBagConstraints();
        gbc.insets = new Insets(5,0,5,0);
        gbc.weighty = 1.0;
        gbc.gridwidth = GridBagConstraints.REMAINDER;
        panel.add(hi, gbc);
        panel.add(lo, gbc);
        panel.add(button, gbc);
        return panel;
    }

    private JPanel getBluePanel() {
        JPanel panel = new JPanel();
        panel.setBackground(Color.blue);
        return panel;
    }

    public static void main(String[] args) {
        JFrame f = new JFrame();
        f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
        f.add(new GettingText().getContent());
        f.setSize(400,400);
        f.setLocationRelativeTo(null);
        f.setVisible(true);
    }
}