>How do I accomplish this ?

InheritEvent is the name of my project.

Base button

using System;
using System.Windows.Forms;

namespace InheritEvent
{
	/// <summary>
	/// Summary description for Class1.
	/// </summary>
	public class MyButtonBase : Button
	{
		public MyButtonBase()
		{
			//
			// TODO: Add constructor logic here
			//
		}

		protected override void OnClick(EventArgs e)
		{
			MessageBox.Show("MyButtonBase Click");
		}

	}
}

Derived button

using System;
using System.Windows.Forms;

namespace InheritEvent
{
	/// <summary>
	/// 
	/// </summary>
	public class MyButtonDerived : InheritEvent.MyButtonBase
	{
		public MyButtonDerived()
		{
			// 
			// TODO: Add constructor logic here
			//
		}

		protected override void OnClick(EventArgs e)
		{
			MessageBox.Show("MyButtonDerived Click");
			base.OnClick(e);
		}

	}
}

Form

using System;
using System.Drawing;
using System.Collections;
using System.ComponentModel;
using System.Windows.Forms;
using System.Data;

namespace InheritEvent
{
	/// <summary>
	/// Summary description for Form1.
	/// </summary>
	public class Form1 : System.Windows.Forms.Form
	{
		private MyButtonBase button1;
		private MyButtonDerived button2;
		/// <summary>
		/// Required designer variable.
		/// </summary>
		private System.ComponentModel.Container components = null;

		public Form1()
		{
			//
			// Required for Windows Form Designer support
			//
			InitializeComponent();

			//
			// TODO: Add any constructor code after InitializeComponent call
			//
		}

		/// <summary>
		/// Clean up any resources being used.
		/// </summary>
		protected override void Dispose( bool disposing )
		{
			if( disposing )
			{
				if (components != null) 
				{
					components.Dispose();
				}
			}
			base.Dispose( disposing );
		}

		#region Windows Form Designer generated code
		/// <summary>
		/// Required method for Designer support - do not modify
		/// the contents of this method with the code editor.
		/// </summary>
		private void InitializeComponent()
		{
			this.button1 = new InheritEvent.MyButtonBase();
			this.button2 = new InheritEvent.MyButtonDerived();
			this.SuspendLayout();
			// 
			// button1
			// 
			this.button1.Location = new System.Drawing.Point(120, 80);
			this.button1.Name = "button1";
			this.button1.TabIndex = 0;
			this.button1.Text = "Base Button";
			// 
			// button2
			// 
			this.button2.Location = new System.Drawing.Point(120, 168);
			this.button2.Name = "button2";
			this.button2.Size = new System.Drawing.Size(72, 32);
			this.button2.TabIndex = 1;
			this.button2.Text = "Derived Button";
			// 
			// Form1
			// 
			this.AutoScaleBaseSize = new System.Drawing.Size(5, 13);
			this.ClientSize = new System.Drawing.Size(352, 349);
			this.Controls.AddRange(new System.Windows.Forms.Control[] {
																		  this.button2,
																		  this.button1});
			this.Name = "Form1";
			this.Text = "Form1";
			this.ResumeLayout(false);

		}
		#endregion

		/// <summary>
		/// The main entry point for the application.
		/// </summary>
		[STAThread]
		static void Main() 
		{
			Application.Run(new Form1());
		}

	}
}