"Add a row to the table" is the wrong way to think about it. Your table represents the collection, and the controller provides information to the table, mediating between the table (view) and assembly (model). Since you mentioned bindings, the collection is probably controlled by NSArrayController. So you want to add a new array (of the type that your array controller controls) to the array of contents of the array controller.
The easiest way: connect the "Add" button to the -add: NSArrayController action. It will add an empty string.
, "" - . , , ( ), , , NSArrayController, -addObject: ( , a -rearrangeObjects, ).