Aquí les copio el ejemplo que viene en el README del .zip.

<?php
require("class.phpmailer.php");

$mail = new PHPMailer();

$mail->IsSMTP(); // set mailer to use SMTP
$mail->Host = "smtp1.example.com;smtp2.example.com"; // specify main and backup server
$mail->SMTPAuth = true; // turn on SMTP authentication
$mail->Username = "jswan"; // SMTP username
$mail->Password = "secret"; // SMTP password

$mail->From = "from@example.com";
$mail->FromName = "Mailer";
$mail->AddAddress("josh@example.net", "Josh Adams");
$mail->AddAddress("ellen@example.com"); // name is optional
$mail->AddReplyTo("info@example.com", "Information");

$mail->WordWrap = 50; // set word wrap to 50 characters
$mail->AddAttachment("/var/tmp/file.tar.gz"); // add attachments
$mail->AddAttachment("/tmp/image.jpg", "new.jpg"); // optional name
$mail->IsHTML(true); // set email format to HTML

$mail->Subject = "Here is the subject";
$mail->Body = "This is the HTML message body <b>in bold!</b>";
$mail->AltBody = "This is the body in plain text for non-HTML mail clients";

if(!$mail->Send())
{
echo "Message could not be sent. <p>";
echo "Mailer Error: " . $mail->ErrorInfo;
exit;
}

echo "Message has been sent";
?>


Viene para PHP 4 o 5/6.
Lo único que necesitás realmente es el class.phpmailer.php (67 Kb.), lo otro ni lo miré…