It appears that PMs are now called "conversations". Hover over the person's avatar (to the left of their post), and a dialog should pop-up with the option "Start conversation." I'm guessing that's how you send a PM now.
Alternatively, you can click on the envelope icon in the menu bar at the top (where you also go to view private messages sent to you). But there, when you "start a new conversation," you'll have to enter the handle of the person you want to message, so make a note of t