Add a Panel and button and use the following code
private void button1_Click(object sender, EventArgs e)
{
TextBox textbox = new TextBox();
textbox.Location = new System.Drawing.Point(10, 25 * panel1.Controls.Count);
textbox.Size = new System.Drawing.Size(70, 20);
textbox.Name = "textbox_" + panel1.Controls.Count + 1;
panel1.Controls.Add(textbox);
}