billibones on "How to write to a database NOT the wordpress database"

Liek Dan said it is best to stay within the WP Db, however easiest way to do what you are wanting to do is to create a file called somthing like: db_connect.php (have all your connections to your DB here (ie. db_name, host, user, pass)

Then (if using a WordPress generated page to collect your users information, you will want to use a plugin like [include it] or create a custom template page based on your theme with your contact form inside of it and make your calls normally as if it were a standard PHP file.)

Something like this:

<? include db_connect.php;

// php / mysql to process collected data
if (isset($formSubmitted))
{
$name = $_POST['name']
$othervariables = $_POST['othervariables'];
$query = 'INSERT ..... $name, $othervariables';
$result = mysql_query($query);
}

// user contact form to collect data
echo 'your form stuff';
-- Note: make sure you write back to the same page by calling:
<form action='<?php echo htmlentities($_SERVER['REQUEST_URI']); ?>' method='POST' enctype='application/x-www-form-urlencoded'>
form submit / clear <inputs>
<input type='hidden' name'formSubmitted' value='Y'>
</form>

?>

Hope this helps.