function validate()
{
   var payment = checkRadio();
   if (payment == false)
   {
      alert("Please select one button")
   }
}

function checkRadio()
{
var payment = document.getElementsByName("payment");
for(i = 0; i < payment.length; i++)
    {
        if(payment[i].checked)
        {
            return true;
        }
        else
        {
            return false;
        }
    }


}

<P> Payment Options:
<INPUT TYPE="Radio" Name="payment" Value="CC">Credit Card
<INPUT TYPE="Radio" Name="payment" Value="DC">Debit Card
<INPUT TYPE="Radio" Name="payment" Value="PP">PayPal
</P>