How to Send a Private Facebook Message
When you first start using Facebook, knowing which message, comment or status updates are being publicly posted and which are private can be confusing, and this confusion has created embarrassing situations for users. If you want to send a private message to a Facebook friend, there's no need to publish anything at all. Instead, send text, photos and files directly to selected friends using Facebook's private messaging and chat features; no one else can view your message.
Sending Private Messages
Click "Messages" from the left pane of your Facebook home page and select "New Message" to open a New Message pane. When you begin typing a Facebook friend's name, a list of suggestions automatically appears; clicking a suggestion addresses the message to only that selected person, but you can optionally add additional recipients. Press "Tab" to move to the bottom composition field to write your message. Click "Add Files" or "Add Photos" to include attachments. Click "Send" to send the message. You can also delete messages in the Messages screen through the Actions menu; doing so removes your copy and does not delete the recipient's copy.
Using the Chat Window
Clicking the bottom "Chat" bar opens the Chat window, so you can send instant messages to online friends, who are marked with green dots by their names. Offline Facebook friends have no icons by their names, but you can still send them private messages, which they'll receive when they next log on. If your friend isn't listed, enter the Facebook friend's name in the search bar. Click a friend's name to open a composition dialog box, write your message and then press "Enter" to communicate only with the selected friend. This option also supports photo attachments and emoticons to convey your feelings.