Thanks to @Samuel Elh I manage to get this done.
I added this to my order-confirmation.php after I included config.php
require ('../wp-blog-header.php');
global $wpdb;
global $current_user;
get_currentuserinfo();
$skrivID = $current_user->ID;
Then the insert query, I added the table I wanted the user ID stored in and used the variable $skrivID as value.
$sql = mysqli_query($db_conn, "
INSERT INTO ordre(
userID,
user_fname,
user_lname,
user_address,
user_email,
user_phone,
service_chosen,
user_note,
order_date,
statusID
)
VALUES(
'".$skrivID."',
'".$_POST['user_fname']."',
'".$_POST['user_lname']."',
'".$_POST['user_address']."',
'".$_POST['user_email']."',
'".$_POST['user_phone']."',
'".$_POST['service_chosen']."',
'".$_POST['user_note']."',
'".date('Y-m-d')."',
'1'
)
");
Ran the form with two different users and voila
Thanks again Samuel!