How Would I Set Up A Layout For A Gui Like This

Your gui split[^]
You can see that there is a panel beneath those 3 red panels.

EDIT: Think about the coding. Separate GUI and Control, set up a service layer.
You're probably writing a description first (big hint!).

EDIT2:
PLease take a look here: A Visual Guide to Layout Managers[^]

and you might try this simple JFrame. Please create yourself a playground project and try things out there:

import java.awt.Color;
import java.awt.GridLayout;

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


public class MyFrame extends JFrame {

	private JPanel panelLeft = new JPanel();
	private JPanel panelRight = new JPanel();
	private JPanel panelLeftTop = new JPanel();
	private JPanel panelLeftBottom = new JPanel();
	
	public MyFrame(){
		this.ignition();
	}
	
	private void ignition() {
		this.setSize(800,600);
		this.setLayout(new GridLayout(1, 2));
		
		panelLeft.setBackground(Color.RED);
		panelRight.setBackground(Color.GREEN);
		panelLeftTop.setBackground(Color.YELLOW);
		panelLeftBottom.setBackground(Color.BLUE);
		
		// inside left panel
		panelLeftTop.setSize(400,300);
		panelLeftBottom.setSize(400,300);
		
		//giving left panel a layout and adding components
		panelLeft.setLayout(new GridLayout(2,1));
		panelLeft.add(panelLeftTop);
		panelLeft.add(panelLeftBottom);
		
		//adding the panels to the JFrame
		this.add(panelLeft);
		this.add(panelRight);
	}

	public static void main(String[] args) {
		new MyFrame().setVisible(true);
	}

}