¿Crear un formulario de búsqueda en PHP para buscar en una base de datos?

prueba esto, déjame saber qué sucede.

Formulario:

<form action="form.php" method="post"> 
Search: <input type="text" name="term" /><br /> 
<input type="submit" value="Submit" /> 
</form>

Formulario.php:

$term = mysql_real_escape_string($_REQUEST['term']);    

$sql = "SELECT * FROM liam WHERE Description LIKE '%".$term."%'";
$r_query = mysql_query($sql);

while ($row = mysql_fetch_array($r_query)){ 
echo 'Primary key: ' .$row['PRIMARYKEY']; 
echo '<br /> Code: ' .$row['Code']; 
echo '<br /> Description: '.$row['Description']; 
echo '<br /> Category: '.$row['Category']; 
echo '<br /> Cut Size: '.$row['CutSize'];  
}

Editar:Lo limpié un poco más.

Final Cut (mi archivo de prueba):

<?php
$db_hostname = 'localhost';
$db_username = 'demo';
$db_password = 'demo';
$db_database = 'demo';

// Database Connection String
$con = mysql_connect($db_hostname,$db_username,$db_password);
if (!$con)
  {
  die('Could not connect: ' . mysql_error());
  }

mysql_select_db($db_database, $con);
?>

<!DOCTYPE html>
<html lang="en">
    <head>
        <meta charset="utf-8" />
        <title></title>
    </head>
    <body>
<form action="" method="post">  
Search: <input type="text" name="term" /><br />  
<input type="submit" value="Submit" />  
</form>  
<?php
if (!empty($_REQUEST['term'])) {

$term = mysql_real_escape_string($_REQUEST['term']);     

$sql = "SELECT * FROM liam WHERE Description LIKE '%".$term."%'"; 
$r_query = mysql_query($sql); 

while ($row = mysql_fetch_array($r_query)){  
echo 'Primary key: ' .$row['PRIMARYKEY'];  
echo '<br /> Code: ' .$row['Code'];  
echo '<br /> Description: '.$row['Description'];  
echo '<br /> Category: '.$row['Category'];  
echo '<br /> Cut Size: '.$row['CutSize'];   
}  

}
?>
    </body>
</html>