If you click on the other's username it will bring 4 options up, their username, view public profile, find more posts and add to contacts. Clicking on public profile will then take you to a screen with tabs "Visitor messages", "About me", "statistics" and "contact info" - use the visitor messages section if you want the message to be sent publicly.
To send privately, hint number 1. in the "contact info" it will have a link saying "send a private message"
OR
To send privately number 2 at the top right hand side of your screen it shows private messages, click this then half way down the page on the left it says "send new message".
General chatter while we wait (and commentary on the "pull out method") (2 Viewers)