When you're logged in - there is a "Messages" link on the top right section of the screen. All past private messages have carried over from the old board. To start a new private message just click on this icon: And type in the username you want to message in the recipients field.
Old board would autofill when you start typing the username - we may bring this back.
There is also a link when you click on their username on their profile page (currently this shows discussions they started).
Right now you need to mark them as read - we'll adjust this.