You are echoing outside the body tag of your HTML. Put your echos there, and you should be fine.
Also, remove the onclick="alert()"
from your submit. This is the cause for your first undefined
message.
<?php
$posted = false;
if( $_POST ) {
$posted = true;
// Database stuff here...
// $result = mysql_query( ... )
$result = $_POST['name'] == "danny"; // Dummy result
}
?>
<html>
<head></head>
<body>
<?php
if( $posted ) {
if( $result )
echo "<script type='text/javascript'>alert('submitted successfully!')</script>";
else
echo "<script type='text/javascript'>alert('failed!')</script>";
}
?>
<form action="" method="post">
Name:<input type="text" id="name" name="name"/>
<input type="submit" value="submit" name="submit"/>
</form>
</body>
</html>