Looking for an explanation (documentation?) for "add(new Surface());"

I found this code online and it works for my application. I'm trying to trace through and understand it more thoroughly. I don't find any documentation that explains the use of the "add(new Surface());" statement. I understand what it does, but here is what I don't understand:

• How does the add() method work without a "SomeObject." in front of it. It seems to assume the add() method is for the object (SampleAddMethod) which contains it. I can't find any documentation on how or when this is valid.
• Why does "super.add(new Surface()); work, but ""SampleAddMethod.add(new Surface());" fail? It seems the add() method is inherited from Component and SampleAddMethod is a JFrame which is a Component.
• Am I correct that (new Surface()) creates an "anonymous class"?

(Sample code below)

package testMainMethod;

import java.awt.Graphics;
import java.awt.Graphics2D;

import javax.swing.JFrame;
import javax.swing.JPanel;
import javax.swing.SwingUtilities;

class Surface extends JPanel {

    private void doDrawing(Graphics g, int x) {
        double xd = (double) x;
        Graphics2D g2d = (Graphics2D) g;

        // Code to draw line image goes here
    }

    @Override
    public void paintComponent(Graphics g) {

        for (int i = 0; i < 512; i++) {
            // super.paintComponent(g); // this erases each line
            doDrawing(g, i);
        }
    }
}

public class SampleAddMethod extends JFrame {

    public SampleAddMethod() {

        initUI();
    }

    private void initUI() {

        setTitle("Lines");
        setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);

        add(new Surface());

        setSize(650, 350);
        setLocationRelativeTo(null);
    }

    public static void main(String[] args) {

        SwingUtilities.invokeLater(new Runnable() {

            @Override
            public void run() {

                SampleAddMethod lines = new SampleAddMethod();
                lines.setVisible(true);
            }
        });
    }

}