By default, the option is available in the basic version to logged-in users when they create a new topic or make a reply to an existing thread.
To enable email notification (i.e. alert me by email when another user posts a reply to this thread): set in setup_options.php, $emailusers to 1, and $genEmailDisable to 0.
It is also possible to allow users to subscribe to a thread without having to post anything. See existing thread "subscribe to a thread without posting a reply
" for details.
All the best,