http://www.swiftmailer.org/wikidocs/v3/basic

Sending an email with Swift Mailer is a simple process. You basically create a new instance of Swift with a connection type of your choice, you then create a message and ask Swift to deliver it to one or more recipients. Perhaps if you're not familiar with OOP this snippet may look a little daunting but it should hopefully soon become familiar to you and feel quite natural. EasySwift, packaged inside the library when you download it, provides a wrapper which makes this even simpler - at the expense of flexibility. Check the EasySwift documentation for more information.

<?php

//Load in the files we'll need
require_once "lib/Swift.php";
require_once "lib/Swift/Connection/SMTP.php";

//Start Swift
$swift =& new Swift(new Swift_Connection_SMTP("smtp.your-host.tld"));

//Create the message
$message =& new Swift_Message("My subject", "My body");

//Now check if Swift actually sends it
if ($swift->send($message, "foo@bar.tld", "me@mydomain.com")) echo "Sent";
else echo "Failed";

This is the most basic way to send an email with Swift without using the EasySwift wrapper (which does make things simpler if you don't like OOP).