Use switch_to_blog( $new_blog_id ), use get_post_meta($post_id, $key ) to get the value of the field, and run restore_current_blog() when you are done.
You could use a site option (add_site_option($option, $value)) and store the values you need in an array there in addition to the post meta field. This would save the rather expensive switch_to_blog() calls.