Advanced Forum adds some functionality to the core forum module by itself but, to really emulate stand alone forum software, you need more modules. Many of the modules here are automatically integrated into Advanced Forum, most by way of the Author Pane module which is a requirement.
This page starts you off with suggested modules but you'll also want to visit the community category in the downloads section for more ideas as new modules are constantly being added. You could also see Drupal modules equivalent to phpBB features.
Enhanced user information and interaction
Administration, and Utility
Flatcomments (Forces all replies to be against the node to avoid deleting issues with hidden threading.)
Edit Limit Enables setting of a time limit for editing original posts (nodes) and replies (comments).