It has become obvious that a lot of members haven't a clue how to send other members a private message, so hopefully this will help
How to send someone a private message than others can't publicly see
1. In the top right of your screen, click on 'Inbox'
2. In the Inbox screen, click on the button on the left hand side 'Start a new conversation'
3. In the Recipients box, start to type in the user name of who you want to send your message to.
4. Either type out the full name, or after a few letters a list of members with those letters will appear. click the one you want
5. You can send a message to multiple users, simply add a comma and a space after the first name and then start the second name.
6. Type your message in the text box below
7. Click Start Conversation.
If you want to add someone to an existing conversation, click on the message, and then the list of people in that conversation will appear down the left hand side. Underneath will be a box 'Add people to this conversation'.
How NOT to send a private message to someone
If you click on a users name, and write a message for that person in the text box provided, that is NOT sending them a private message, but posting a message on their Wall. By doing this, everyone else can see that message if they click on that persons name, or through the Activity button. The user you will be sending it to will also not receive any notification you have done this, so probably won't even notice you have left them a message.
Hope that helps