Wordpress - Proper formatting of post_date for wp_insert_post?

If you don't add a post_date then WordPress fills it automatically with the current date and time.

To set another date and time [ Y-m-d H:i:s ] is the right structure. An example below with your code.

$postdate = '2010-02-23 18:57:33';

$new_post = array(
   'post_title'    =>   $title,
   'post_content'  =>   $description,
   'post_date'     =>   $postdate,
   'post_status'   =>   'publish',
   'post_parent'   =>   $parent_id,
   'post_author'   =>   get_current_user_id(),
);

//SAVE THE POST
$pid = wp_insert_post($new_post);

to convert your date into Wordpress (MySQL DATETIME) format, try this:

$date_string = "Sept 11, 2001"; // or any string like "20110911" or "2011-09-11"
// returns: string(13) "Sept 11, 2001"

$date_stamp = strtotime($date_string);
// returns: int(1000166400)

$postdate = date("Y-m-d H:i:s", $date_stamp);
// returns: string(19) "2001-09-11 00:00:00"

$new_post = array(
    // your other arguments
   'post_date'     =>   $postdate
);

$pid = wp_insert_post($new_post);

or course if you want to really be sexy do this:

'post_date'     => date("Y-m-d H:i:s", strtotime("Sept 11, 2001"))

You can't format the $_POST['date'] like this... You'll have to run the value from $_POST['date'] through something like $postdate = date( $_POST['date'] )... There's also the possibility to call get_option for the blog settings. See Option Reference in Codex.