From the restaurant list, you can either go to each place’s Facebook page and order there, or select Start Order. You select the items you want to order on the restaurant’s menu, then you select a tip, and pay for it within the app.
That said, it doesn’t work for everybody yet. Some, like me, might be told that there are no nearby restaurants who will deliver (it doesn’t specify whether that means “deliver at all” or “deliver via Facebook”). I know that’s not the case for my area, so I have to assume it’s a flaw in the system.
The option is the fruit of a partnership between Facebook and food delivery sites Delivery.com and Slice. Previously, you’d have to go to a specific restaurant’s Facebook page in order to order from them.