How to draw directly on the Windows desktop, C#?

Try the following:

using System;
using System.Drawing;
using System.Drawing.Drawing2D;
using System.Runtime.InteropServices;

class Program {

    [DllImport("User32.dll")]
    static extern IntPtr GetDC(IntPtr hwnd);

    [DllImport("User32.dll")]
    static extern int ReleaseDC(IntPtr hwnd, IntPtr dc);

    static void Main(string[] args) {
        IntPtr desktop = GetDC(IntPtr.Zero);
        using (Graphics g = Graphics.FromHdc(desktop)) {
            g.FillRectangle(Brushes.Red, 0, 0, 100, 100);
        }
        ReleaseDC(IntPtr.Zero, desktop);
    }
}