A form's Opacity property determines how opaque it is. Opacity = 1 means the form is opaque and Opacity = 0 means the form is transparent. Values between 0 and 1 make a translucent form. (Note that at design time the Properties window displays Opacity values between 0% and 100% instead of between 0 and 1.)

When you click this example's Close button, the code enables a Timer control that reduces the form's Opacity until it disappears.

// Make the form disappear.
private void btnClose_Click(object sender, EventArgs e)
{
    tmrFade.Enabled = true;
}

// Decrease the form's opacity by 20%.
private void tmrFade_Tick(object sender, EventArgs e)
{
    Opacity -= 0.2;
    if (Opacity <= 0) Close();
}