How to set custom cookies in WordPress after a form is filled on a page

Your page-xyz.php has to look like this:

$cookie_set = isset( $_COOKIE['mycookie'] );

if ( $_SERVER['REQUEST_METHOD'] == 'POST' ) :
    // exec your mysql queries and do else stuff...

    // after it set your cookie
    setcookie('mycookie', 'some value');
    $cookie_set = true;
endif;

if ( $cookie_set ) :
    // render your content here
else :
    // render your form here
endif;