Show custom messages on dashboard menu page

There is number of hooks dedicated for displaying admin notices in admin-header.php:

if ( is_network_admin() )
    do_action('network_admin_notices');
elseif ( is_user_admin() )
    do_action('user_admin_notices');
else
    do_action('admin_notices');

do_action('all_admin_notices');

Codex has basic example, but admin markup is not very stable so you might need to research native notices in current version to properly replicate it.