After you submit your form, on the target page you can use similar to the following to mail. This assumes that mail is working correctly to begin with.
$msg = "Thank you for registering ".$SOMEVARIABLE." for participation!\n\n".
"You registered the following information...\n\n".
$var1 ."\n".
$var2 ."\n".
$var3 ."\n".
$var4 ."\n\n".
"BLAH BLAH BLAH....\n\n".
"BLAH BLAH BLAH BLAH....\n\n".
"Again, thanks for your participation!\n\n".
"Sincerly,\n".
"TheSender\n";
mail("TARGET@EMAILGOES.HERE", "SUBJECT GOES HERE", $msg,"From: FRIENDLY NAME HERE\nReply-To: [email]you@wherever.net[/email]\nX-Mailer: PHP/" . phpversion());