How can I have a private conversation on facebook
In order to have a private conversation on Facebook you need to go to your "inbox". When you send messages using the inbox, you and the recipient are the only ones able to view the message. For instructions on how to do this, check http://www.ehow.com/video_2201976_use-facebook-inboxuse-facebook-inbox.html.
Doing chat like instant messaging or through a message. Do not write on the persons wall or status.