Just set the permissions on all Geeklog objects (stories, topics, blocks, etc.) such that anonymous users can't see them (uncheck the "Anonymous R" checkbox). Leave the "User Functions" block visible for anonymous Users, though, since it's used as the login form when you're not logged in.
You can also prevent access to the calender, links section, search, etc. by setting the $_CONF['loginrequired'] flags (in config.php) accordingly.
The only problem is what to display to anonymous users. With the above, they will only see the login form and a note saying that they don't have permission to view stories. With Geeklog 1.3.8 and Static Pages 1.3 you would be able to create a static page to be displayed to anonymous users. Not sure if that's possible with Static Pages 1.2 ...
bye, Dirk