How to get login data (session) outside WordPress?

I guess WP uses a PHP session (or a cookie) to save login data, right?

I have a website, which uses WP as a CMS, but display (and create) content from outside. I allow anonymous posts, by simply not passing $post['post_author'] to wp_insert_post()

However, I also want to make users (that are registered in WP) to be able to login in mysite/wp/wp-login.php, than redirect to mysite/mypage.php, and get the user id from session or cookie.

How do I do that?

Edit

The code:

include( 'wp/wp-load.php');  
global $current_user;
get_currentuserinfo();
print_r($current_user);

this prints an empty WP_User Object:

WP_User Object ( [data] => [ID] => 0 [caps] => Array ( ) [cap_key] => [roles] => Array ( ) [allcaps] => Array ( ) [filter] => ) 

Although I’m logged in in WP.

P.S.
Now that I saw wp-login-form in tags, which gave me a better idea.

Can I put a login form to my page (outside wp) ? This would surely be better, since it wouldn’t require the users to redirect.

I want minimum (ideally zero) interaction between mysite/wp and visitors (including Google Bot).