How do I prevent mails sent through PHP mail() from going to spam?

There is no sure shot trick. You need to explore the reasons why your mails are classified as spam. SpamAssassin hase a page describing Some Tips for Legitimate Senders to Avoid False Positives. See also Coding Horror: So You'd Like to Send Some Email (Through Code)

You must to add a needle headers:

Sample code :

$headers = "From: [email protected]\r\n";
$headers .= "Reply-To: [email protected]\r\n";
$headers .= "Return-Path: [email protected]\r\n";
$headers .= "CC: [email protected]\r\n";
$headers .= "BCC: [email protected]\r\n";

if ( mail($to,$subject,$message,$headers) ) {
   echo "The email has been sent!";
   } else {
   echo "The email has failed!";
   }
?>