You can check for
$_SERVER['REMOTE_USER'], which tells you if a user is logged in. The following, for instance, will conceal all the action links except "back to top" in the new dokuwiki template. Search the forum for _SERVER['REMOTE_USER'] for other examples and explanations.
<?php
if ($_SERVER['REMOTE_USER']) {
tpl_action('edit', 1, 'li', 0, '<span>', '</span>');
tpl_action('revert', 1, 'li', 0, '<span>', '</span>');
tpl_action('revisions', 1, 'li', 0, '<span>', '</span>');
tpl_action('backlink', 1, 'li', 0, '<span>', '</span>');
tpl_action('subscribe', 1, 'li', 0, '<span>', '</span>');
}
tpl_action('top', 1, 'li', 0, '<span>', '</span>');
?>
These types of links and buttons will be found in either main.php or the above in tp_header.php, depending on your template.